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Data hiding is a technique that conceals a given mystery message within a cover medium in a secure way. It provides an additional security layer to protect valuable data embedded into the cover medium and transferred via the Internet. Steganography approaches based on transform domains are the most popular due to their high security in image steganography. Unfortunately, these approaches have two major existing disadvantages significant computing power and limited embedding capacity. To overcome these drawbacks, in this paper a hybrid scheme based on Lah transform is proposed. At first, the Lah transform is utilized to generate the Lah coefficients from the considered 4-pixel blocks of the considered cover image. Then, these Lah components are modified to embed the valuable data. For embedding rates equal to or less than 0.5 bpp, a modified Hamming code based method (MHCBM) is employed to conceal the given message bits in the generated Lah components. For payload larger than 0.5 bpp into the Lah transform coefficients, a modified LSB matching revisited approach (MLSBMR) is used. This principle allows us to minimize statistical distortion to the stego images, while at the same time enhancing the security of the hidden message against statistical steganalysis approaches. Experimental results indicated that the proposed scheme achieved better perceptual quality and higher security performance compared to the existing Lah transform based method and the relevant integer based transform approaches. [ABSTRACT FROM AUTHOR]

A packing k -coloring of a graph G is a mapping assigning a positive integer (a color) from the set 1 , ... , k to every vertex of G such that every two distinct vertices of color c are at distance at least c + 1. The minimum value k such that G admits a packing k -coloring is called the packing chromatic number of G. In this paper, we continue the study of the packing chromatic number of hypercubes and we improve the upper bounds reported by Torres and Valencia-Pabon (2015) by presenting recursive constructions of subsets of distant vertices making use of the properties of the extended Hamming codes. We also answer in negative a question on the packing chromatic number of Cartesian products raised by Brešar et al. (2007). [ABSTRACT FROM AUTHOR]

Let λ = λ0 + uλ1 + ⋯ + uk−1λ k−1 be a Type 1 unit in ℜk = 픽pm + u픽pm + ⋯ + uk−1픽 pm(uk = 0), where p is an odd prime, m is a positive integer and λ0,λ1,…,λk−1 ∈ 픽pm,λ0≠0,λ1≠0. In this paper, we give the complete structure of all Type 1 λ-constacyclic codes and their duals of length 8ps over the finite commutative chain ring ℜk in terms of their generator polynomials. Using this structure, we determine the Hamming distance and the Rosenbloom–Tsfasman (RT) distance of all Type 1 λ-constacyclic codes. For pm ≡ 1(mod 4) and a unit λ ∈ ℜ2, we determine the b -symbol distances of all λ-constacyclic codes of length 8ps over ℜ2, where b ≤ 8. As illustrations, we provide several λ-constacyclic codes with new parameters with respect to Hamming, RT and b-symbol metrics. MDS codes are widely recognized for their optimal error-correction capability, and MDS b-symbol codes are generalization of MDS codes. We found some MDS b-symbol constacyclic codes of length 8ps over ℜ2. Additionally, for pm ≡ 1(mod 4), we provide a decoding algorithm for Type 1 constacyclic codes of length 8ps over ℜk with respect to the Hamming, RT and b-symbol metrics. [ABSTRACT FROM AUTHOR]

This article presents a novel system, LLDPC,1 which brings Low-Density Parity-Check (LDPC) codes into Long Range (LoRa) networks to improve Forward Error Correction, a task currently managed by less efficient Hamming codes. Three challenges in achieving this are addressed: First, Chirp Spread Spectrum (CSS) modulation used by LoRa produces only hard demodulation outcomes, whereas LDPC decoding requires Log-Likelihood Ratios (LLR) for each bit. We solve this by developing a CSS-specific LLR extractor. Second, we improve LDPC decoding efficiency by using symbol-level information to fine-tune LLRs of error-prone bits. Finally, to minimize the decoding latency caused by the computationally heavy Soft Belief Propagation (SBP) algorithm typically used in LDPC decoding, we apply graph neural networks to accelerate the process. Our results show that LLDPC extends default LoRa's lifetime by 86.7% and reduces SBP algorithm decoding latency by 58.09×. [ABSTRACT FROM AUTHOR]

Rotating Polarization Wave (RPW) is a novel Low Power Wide Area Networks (LPWAN) technology for robust connectivity and extended coverage area as compared to other LPWAN technologies such as LoRa and Sigfox when no error detection and correction is employed. Since, IoT and Machine-to-Machine (M2M) communication demand high reliability, RPW with error correction can significantly enhance the communication reliability for critical IoT and M2M applications. Therefore, this study investigates the performance of RPW with single bit error detection and correction using Hamming codes to avoid substantial overhead. Hamming (7,4) coded RPW shows a remarkable improvement of more than 40% in error performance compared to uncoded RPW thereby making it a suitable candidate for IoT and M2M applications. Error performance of coded RPW outperforms coded Chirp Spread Spectrum (CSS) modulation used in LoRa under multipath conditions by 51%, demonstrating superior adaptability and robustness under dynamic channel conditions. These findings provide valuable insights into the ongoing developments in wireless communication systems whilst reporting Q-RPW model as a new and effective method to address the needs of developing LPWAN and IoT ecosystems. [ABSTRACT FROM AUTHOR]

The Hamming code or Linear block code is used in communication to identify and repair errors. Redundancy bits are introduced to the Hamming communication network (HCN) for error detection and correction. It can detect two errors and correct one error. Quantum-dot Cellular Automata (QCA) is used for designing circuits with high switching speed and low energy dissipation. This work proposes a cost-effective QCA-based (7, 4) Hamming encoder and decoder design. Hamming encoder is designed using coplanar structure and the error detector used in Hamming decoder uses a multilayer structure. The effort is to optimize the area, cost, and energy dissipation. The work proposes a coplanar (7, 4) Hamming encoder and decoder. Hamming decoder is implemented in two parts a syndrome calculator and an error detector. Proposed (7, 4) Hamming encoder circuit reduces cell count by 49.47% compared to [1] and 9.52% compared to [12]. The proposed (7, 4) syndrome calculator has reduced cell count by 56.54%, an 11.11% reduction in total area compared to [1]. The proposed design reduces the cell area, QCA cost, and also energy dissipation. The designs are realized and QCA parameters are assessed in QCADesigner2.0.3 and energy is analyzed in QCADesigner-E. [ABSTRACT FROM AUTHOR]

Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight in this code support a 2-design. In this paper, we study this family of extended primitive cyclic codes in more details. The weight distribution is determined and the parameters of the related 2-designs are also given. Moreover, we prove that the minimum weight codewords in this code support a 3-design when p = 2 , which gives an affirmative answer to Heng's conjecture. [ABSTRACT FROM AUTHOR]

In recent years, data hiding techniques have emerged as a prominent area of research due to the increasing demand for information security. Existing data hiding techniques typically do not prioritize the verification of the correctness of the extracted data, nor do they attempt to rectify any erroneous information extracted. This paper presents a simple yet effective method by which a recipient can perform error detection and correction on extracted data. Prior to data embedding, a preprocess is applied to secret data. After converting the secret data to a data stream, a data hider categorizes adjacent and identical bits within the data stream into groups. The number of these bits is then recorded as an indicator to extract information and perform error detection and correction. The number of bits in each group is adjusted to ensure that it is an odd number. Moreover, the collected indicator data stream is encoded using (7,4) Hamming code to compact the recorded information. Finally, the concatenation of the encoded indicator and the encoded secret is embedded into the multiple least significant bits (LSBs) of the original image pixels. As for the receiver, error correction can be applied based on the indicator after the extraction of the encoded data. Experimental results demonstrate that this method allows the data receiver to detect and correct errors while maintaining a certain level of embedding capacity and image quality. In terms of image quality, this method exhibits superior performance compared to existing research when the embedded data volume is relatively small. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient design of Hamming (11, 7) encoder utilising Full Swing-Gate Diffusion Input (FS-GDI) approach in 65 nm technology nano-size node. The proposed design of Hamming codes aims to improve the power and area efficiency through reducing of transistors count by employing power-efficient logic style. Encoding circuits of Hamming code (11, 7) and (7, 4) are designed using the various traditional and proposed approaches. The amount of consumed power, delay time, Power Delay Product (PDP) and hardware simplicity are employed as a metrics for evaluating the efficiency of the proposed designs of encoding circuits. The simulation experiments are executed utilising Cadence Virtuoso simulator package. These experiments revealed that the proposed designs of Hamming encoding circuits achieve delay time reduction by 50.91% and 20% for Hamming codes (7, 4) and (11, 7), respectively. Also, hardware (H/W) simplicity and area efficiency of the circuits are improved by 50% compared to CMOS-based circuits. From the results analysis, the proposed FS-GDI based Hamming encoding circuits achieve efficient power and delay optimising. Hence, the power consumption, delay and area in communications systems and DSP circuits due to encoding process are reduced. The whole performance of DSP circuits can be more power/area efficient. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to further study the structure, parameters and constructions of the recently introduced minimal codes in the sum‐rank metric. These objects form a bridge between the classical minimal codes in the Hamming metric, the subject of intense research over the past three decades partly because of their cryptographic properties, and the more recent rank‐metric minimal codes. We prove some bounds on their parameters, existence results, and, via a tool that we name geometric dual, we manage to construct minimal codes with few weights. A generalization of the celebrated Ashikhmin–Barg condition is proved and used to ensure the minimality of certain constructions. [ABSTRACT FROM AUTHOR]

Copyright of Journal of South China Normal University (Natural Science Edition) / Huanan Shifan Daxue Xuebao (Ziran Kexue Ban) is the property of Journal of South China Normal University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Numerous soft faults in SRAM memory emerge as technological innovations scales down, resulting in single and several cell upsets. The increased use of transistors in space applications has rendered semiconductor devices more vulnerable to soft errors caused by harm from radiation. A single event upset (SEU) is occurring whenever a soft error produces a tiny bit flipped in a storage device. Because SEU faults affect system performance, they must be addressed as soon as possible. Error-correcting codes, like the method known as (7,4) hamming codes, were devised and their decoding and encoding procedures were verified. It also used to detect single errors that can be fixed. It also helps detect double errors, SECDED however repair of double errors is tough. The decoding and encoding techniques of these approaches were investigated, and all computational findings had been verified and executed in a Xilinx NEXYS 4 DDR FPGA board. [ABSTRACT FROM AUTHOR]

Shape recognition is an active research topic in the field of computer vision and graphic computing. Nevertheless, existing methods are still poor in accuracy and efficiency in some extent, which greatly limits their application in computer vision system. This paper investigates the restraint of feature structure that intrinsically deteriorates recognition performance. Furthermore, we propose a fast shape recognition method based on a bi-level restraint reduction of contour coding (CC2RR), which provides more effective theoretical support for the practical application of the visual algorithm. CC2RR reduces restraint performed from contour feature extraction and expression, respectively. First, for shape contour, the restraint of contour feature extraction is reduced by transforming the direction of contour points to contour segments; second, for the encoded contour segment, the restraint of the contour feature expression is reduced; in other words, the current direction is reduced to the previous and the next direction. Guided by these insights, Hamming code distance is used to match the coding features after the twofold restraint reduction, and the results are obtained. Experimental results verify that the method significantly improves the performance, which runs up to 500 times faster than the existing description methods based on shape contours while increasing robustness. This makes the method useful in practical software system. [ABSTRACT FROM AUTHOR]

In the present paper, we give harmonic weight enumerators and Jacobi polynomials for the first-order Reed–Muller codes and the extended Hamming codes. As a corollary, we show the nonexistence of combinatorial 4-designs in these codes. [ABSTRACT FROM AUTHOR]

We consider the class of linear antipodal two-weight rank metric codes and discuss their properties and characterization in terms of t-spreads. It is shown that the dimension of such codes is two and the minimum rank distance is at least half of the length. We construct antipodal two-weight rank metric codes from certain MRD codes. A complete classification of such codes is obtained, when the minimum rank distance is equal to half of the length. As a consequence of our construction of two-weight rank metric codes, we get some explicit two-weight Hamming metric codes. [ABSTRACT FROM AUTHOR]

The object of the study is the IOT system for monitoring the state of objects. The problem being solved is the development of an innovative method of detecting and correcting data transmission errors in the networks of Internet of Things systems. The essence of the results is that a method of detecting and correcting multiple transmission errors during byte-by-byte transmission of a block of information has been developed. The method is distinguished by an original coding scheme, which involves the calculation of control bits, as well as the shuffling of block bits by performing bit shift operations. The peculiarity of the method is that any bit can be distorted when transmitting a code word, but it belongs to different code combinations of the Hamming code. This allows multiple data transmission errors to be detected and corrected during decoding, and multiple errors of different bytes belonging to the same block can be corrected. Simple algorithms for encoding and decoding procedures have been developed, and programs for information block encoding procedures and decoding procedures with error detection and correction have been developed. A software model of the data transmission channel was also developed with the possibility of introducing multiple errors when simulating the data transmission process. All programs are developed in Python, although other languages are possible. An experiment was conducted using the developed software model of the data transmission channel. The efficiency of the developed method has been experimentally confirmed and it has been proven that its use increases the immunity of the data transmission channel. This is due to the fact that the developed method allows detecting and correcting all code word transmission errors with a multiplicity from 1 to 8, which was confirmed experimentally. The main field of use of the developed method is considered to be IoT system networks. First of all, systems for monitoring the state of objects. [ABSTRACT FROM AUTHOR]

A lower bound is presented for the minimal number of filled cells in a maximal partial Latin hypercube of dimension d and order n. The result generalises and extends previous results for d = 2 (Latin squares) and d = 3 (Latin cubes). Explicit constructions show that this bound is near-optimal for large n > d . For d > n , a connection with Hamming codes shows that this lower bound gives a related upper bound for the same quantity. The results can be interpreted in terms of independent dominating sets in certain graphs, and in terms of codes that have covering radius 1 and minimum distance at least 2. [ABSTRACT FROM AUTHOR]

Steganography and secret sharing are schemes to increase the security of private information against attackers. Steganography emphasizes secrecy while secret sharing distributes the secret key in shares that are conditionally classified to reconstruct the original secret. This paper introduces a counting‐based secret sharing scheme that aims to reduce the computational complexity for longer keys, thereby providing a practical steganographic approach for efficient sharing. The scheme integrates counting‐based secret sharing with integer wavelet transform (IWT) and steganography. The subscriptions created using the Hamming code are embedded in the cover image. Using this method, IWT significantly reduces the occurrence of common rounding errors. As a result, secret key extraction becomes very accurate and eliminates the need to access the original images. This design, using secret sharing based on counting, not only has simplicity and efficiency, but also features such as flexibility, scalability, and lack of central authority. In addition, high‐quality steganography was obtained for keys with lengths of 64, 256, 512, 1024, and 3072, showing an average PSNR=80.11 in different color images. This outstanding performance makes it a highly efficient alternative to previous designs, representing a groundbreaking contribution with significant public interest in the field. [ABSTRACT FROM AUTHOR]

This paper provides an introductory overview of cyclic codes of Hamming type and showcases their effectiveness in detecting and correcting errors in digital communications. Thus, a Progressive Web Application has been developed through React.js and p5.js JavaScript libraries to simulate the coding operations using Linear Feedback Shift Registers. This GUI serves an educational purpose, being used in Information Transmission Theory laboratories so that students could easier comprehend this particular coding scheme. The results obtained highlight the efficiency of developed software application in the e-learning process of cyclic code of Hamming type and its adeptness in error detection and correction within digital communications. [ABSTRACT FROM AUTHOR]

Soft errors are the most common aspect of errors that are incurred in the memory devices during transmission. The common and fundamental reason of these soft errors is radiation that produces leakage of current and results in misleading information which is sent to various transmission stations via satellite and microwave communication. In this paper, the real-time embedded system is designed and implemented to mitigate the soft error using hybrid Hamming code. The work also develops the hardware system for soft error mitigation. The designed system is compared with the other coding schemes that are commonly available for error mitigation. The performance of real-time embedded system for soft error mitigation is carried out using signal-to-noise ratio and other performance metrics. The timing diagram analysis is the key metrics of the paper that defined the performance of the designed soft error mitigation design using the proposed technique. Furthermore, the results of the designed systems are demonstrated using bit error probability, Pb and channel symbol error probability (CSEP). The impact of the designed system will be that from now onwards using the proposed system, the soft error produced due to radiation and other reasons would not affect too much on transmission and reception of important data via satellite and microwave communication. [ABSTRACT FROM AUTHOR]

Multi-view subspace clustering, which partitions multi-view data into their respective underlying subspaces, has achieved the remarkable clustering performance by extracting abundant complementary information from data of different views. However, existing subspace clustering methods almost suffer from very heavy computational burden that restricts their capacity on computational efficiency for large-scale datasets. Recently, hashing/binary code learning has attracted intensive attentions due to fast Hamming distance computation and much less storage requirement, but existing related research does not explore underlying subspace clustering structure well that widely exists in real-world data. In order to handle the both issues, in this paper, we propose a multi-view subspace clustering method named Hashing Multi-view Sparse Subspace Learning (HMSSL). HMSSL incorporates multi-view binary code learning and binary sparse subspace learning with a "thin" dictionary into a unified framework. HMSSL encodes multi-view real-valued features in the original space into compact common binary codes in the Hamming space for fast Hamming distance computation by multi-view binary code learning and learns the binary sparse subspace representation matrix for exploring the underlying subspace clustering structure efficiently and effectively by binary sparse subspace learning with a "thin" dictionary matrix. All the columns of the dictionary matrix are randomly and uniformly sampled from all the columns of the compact common binary code matrix. We design an effective binary optimization algorithm based on alternating direction multiplier method and analyze its time complexity. Extensive experiments performed on six benchmark multi-view datasets demonstrate the effectiveness of HMSSL in comparison with ten state-of-the-art baselines in this field. [ABSTRACT FROM AUTHOR]

Copyright of Revista Foco (Interdisciplinary Studies Journal) is the property of Revista Foco and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study the probability of an undetected error for general q-ary codes. We give upper and lower bounds on this quantity, by the Linear Programming and the Polynomial methods, as a function of the length, size, and minimum distance. Sharper bounds are obtained in the important special case of binary Hamming codes. Finally, several examples are given to illustrate the results of this paper. [ABSTRACT FROM AUTHOR]

A novel data hiding method based on overlapped (7,4) Hamming code is proposed in this paper. 11-bit codewords are constructed from two overlapped (7,4) Hamming codes, and then a look-up table of 11-bit codeword is established, from which the suitable 11-bit codeword can be selected to minimize the stego image distortion. Because Hamming codes, rather than the bits of the pixels, are overlapped, the embedding capacity is improved remarkably. Two transferring stages are jointly optimized to minimize the stego image distortion and improve the visual quality. Several construction modes are designed and available to balance the embedding capacity and visual quality, so the modes can be selected flexibly. The systematical theoretical analysis consistent with the experimental results solidly confirms the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

Purpose: The main aim of this study is to elaborately examine the error correction technology for global navigation satellite system (GNSS) navigation messages and to draw a conceptual decision support framework related to the modernization of the GNSS and other systems. Design/methodology/approach: The extensive simulation model developed in Matrix Laboratory (MATLAB) is used to evaluate the performance of forward error correction (FEC) codes such as Hamming, Bose–Chaudhuri–Hocquenghem, convolutional, turbo, low-density parity check (LDPC) and polar codes under different levels of noise. Findings: The performance and robustness of the aforementioned algorithms are compared based on the bit length, complexity and execution time of the GNSS navigation message. In terms of bit error rate, LDPC coding exhibits more ability in the robustness of the navigation message, while polar code gives better results according to the execution time. Practical implications: In view of future new GNSS signals and message design, the findings of this paper may provide significant insight into navigation message modernization and design as an important part of GNSS modernization. Originality/value: To the best of the authors' knowledge, this is the first study that conducts a direct comparison of various FEC algorithms on GNSS navigation message performance against noise, taking into consideration turbo and newly developed polar codes. [ABSTRACT FROM AUTHOR]

Graphical designs are the extension of spherical designs to finite graphs from the viewpoint of quadrature formulas. In this paper, we investigate optimal graphical designs on hypercubes, especially the conjecture proposed by Babecki that the Hamming code is an optimal graphical design on the hypercube. We prove that this conjecture is not true using certain binary t-error-correcting BCH codes. We also obtain extremal graphical designs on the furthest distance graph of 13 families of distance-regular graphs with classical parameters. This generalizes the result that any 1-intersecting family achieving Erdös–Ko–Rado type bound is an extremal graphical design on the Kneser graph. [ABSTRACT FROM AUTHOR]

Among Non-Volatile Memories (NVMs), PCMs are considered the best alternative to DRAM (dynamic random-access memories). As a result of its superior performance and scalability, there are several advantages over DRAM, including lower leakage and energy consumption, higher cell number, and smaller cells. This kind of memory does, however, suffer from a long write latency. In this article, we present a technique to reduce write latency by reducing the number of SET operations. The proposed method is an improved Write Time Speed-up (WTS) code scheme. In the proposed scheme, a new code based on hamming weight is given, and an appropriate algorithm is written to reduce the number of SET operations. Compared with current methods, the proposed scheme decreased SET and RESET operations by 3.9 percent, SET operations by 3.3 percent, and power consumption by 2.6 percent. Visual Basic 6 and GEM 5 simulations are used to simulate the suggested method. [ABSTRACT FROM AUTHOR]

We classify all linear completely regular codes which have covering radius and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights and . [ABSTRACT FROM AUTHOR]

Data hiding and reversible data hiding research has primarily focused on grayscale and color images, because binary and halftone images are prone to visual distortion caused by a small number of errors in pixel representation. As a result, reversible data hiding is more useful than halftone-based data hiding. This study proposes an investigation of encrypted halftone images based on dual reversible data hiding, which improves the reversibility and security of the image by utilizing a dual cover image. Since halftone images are adequately compressed, they are beneficial in low-channel-bandwidth environments. Hamming code (HC) (7,4) is applied to each block of the halftone image to hide the secret data, and two halftone images are recorded and sent to different receivers at the end of the embedding process. Recipients can use the proposed method and the two marked images to extract the message and recover the cover halftone image. The proposed data hiding method can enhance the quality of the decrypted image by appropriately increasing the block size, and conversely, sufficiently large amounts of data can be hidden by reducing the block size. The experimental results provide evidence of the effectiveness of the proposed method in terms of both image quality and the embedding rate. [ABSTRACT FROM AUTHOR]

A graphical design is a subset of graph vertices such that the weighted averages of certain graph eigenvectors over the design agree with their global averages. We use Gale duality to show that positively weighted graphical designs in regular graphs are in bijection with the faces of a generalized eigenpolytope of the graph. This connection can be used to organize, compute and optimize designs. We illustrate the power of this tool on three families of Cayley graphs – cocktail party graphs, cycles, and graphs of hypercubes – by computing or bounding the smallest designs that average all but the last eigenspace in frequency order. [ABSTRACT FROM AUTHOR]

Fragile watermarking is embedding a watermark in a media (an image in this paper) such that even small changes, called tamper, can be detected or even recovered to prevent unauthorized alteration. A well-known category of spatial fragile watermarking methods is based on embedding the watermark in the least significant bits of the image to preserve the quality. In addition, Hamming code is a coding algorithm in communication that transmits the data bits by augmenting some check bits to detect and recover single-bit modifications precisely. This property was previously used to detect and perfectly recover the images modified by small tampers less than a quarter of the image in diameter. To achieve this goal, the Hamming code is applied on a distributed pixel, bits of which are gathered from sufficient far pixels in the image. It guarantees that such tampers can toggle at most one bit of each distributed Hamming code that is recoverable. It was the only guaranteed perfect reconstruction method of small tampers, based on our knowledge. In this paper, the method has been extended to support distortion in two bits of a Hamming code by the use of common structures of distributed codes. It guarantees the recovery of tampers less than half of the image in width and height. According to the experimental results, the proposed method achieved better performance, in terms of recovering the tampered areas, in comparison to state-of-the-art. [ABSTRACT FROM AUTHOR]

In this paper, a new audio watermarking scheme is proposed that addresses the synchronization problem using an adaptive filter. To spread the watermark energy across the spectrum of the host audio signal, the scheme uses Hamming coding, convolutional encoding, and generalized PN sequence generation and for watermark recovery, the scheme utilizes Viterbi decoding. Also, the watermark cannot be detected either statistically or perceptually. To increase the watermark embedding capacity, the watermark is embedded in certain areas of the host signal, which increases the masking threshold. By using a high masking threshold, the adaptive watermark insertion, blind detection, robustness, and capacity of watermarking are enhanced in comparison to similar methods. Finally, experimental results show that in addition to guaranteeing an error bit rate (BER) of almost 0 for non- and minor-attack conditions, the BER is substantially improved in the case of low-pass filtering at a cutoff frequency as low as 3.2 KHz. [ABSTRACT FROM AUTHOR]

Molecular Communication (MC) is a multidisciplinary branch that lies at the junction of nano, bio and communication technology. MC is evolving to serve almost every field of humanity, be it biomedical, be it environment or be it security against NBC attack. On the other hand, MC lags in technological demonstration and development level. However, like any communication system, Error Correction Code (EEC) play vital role in MC system, to improve the system performance. Recently, literatures have presented on VLSI implementation of Cyclic Reed–Muller (C-RM) and Hamming code. However, VLSI implementation and demonstrations of Self-Orthogonal Convolution Codes (SOCC) and Low-Density Parity Check (LDPC) codes, which outperform over others, are not available in the literatures. Therefore, this paper implements SOCC and LDPC codes in Tanner EDA Tool followed by presenting the power consumption and delay of respective codes. More specifically, this paper presents design and implementation of encoder and decoder of SOCC for MC system using Tanner EDA Tool and demonstrated the performance in terms of power consumption and delay. In addition, similar analysis is presented for LDPC code. It is important to mention that implemented decoder of each of the LDPC and SOCC codes is employing newly presented MLG circuit in is manuscript. Finally, power consumption and delay of SOCC and LDPC are compared with those of available ECCs in literatures. [ABSTRACT FROM AUTHOR]

Error-free communication is crucial for modern electronic devices. Error detection and correction mechanisms are essential to ensure accurate information transmission. With the increasing usage of mobile devices and integrated circuits operating at higher speeds, energy efficiency has become an important design consideration. This study presents carbon nanotube field-effect transistor (CNTFET)-based Hamming Error Detection and Correction circuits and compares them with complementary metal-oxide semiconductor (CMOS)-based counterparts in terms of power efficiency and delay. CNTFETs are more power-efficient and faster than CMOS transistors, making them ideal building blocks for logic circuits. The proposed circuits were simulated using HSPICE. Compared with CMOS circuits, the CNTFET designs consumed less power, had lower delays, and smaller power-delay products. The proposed error detection and correction circuits are suitable for power-efficient and portable systems [ABSTRACT FROM AUTHOR]

Quantum-dot Cellular Automata (QCA) are preferred for realizing logic circuits at nanoscale dimensions along with a high level of integration and minimal energy consumption. Hamming code is a set of entropy codes used for error detection and correction in communication systems. Error detection and correction is carried out with the help of parity bits which are appended with the original bits. Designing a Hamming encoder in nanoscale has its own merits such as optimized area, reduced energy dissipation and lower QCA cost. This work proposes two QCA-based (7, 4) Hamming encoder designs; multilayer (proposed1) and coplanar (proposed-2) structure with area and energy analysis. Proposed-1 encoder has achieved reduction of cell area by 12.5 %, 34.58 % in terms of cell count, and reduction in total energy dissipation of 26.8 % when compared to reference encoder. Proposed2 encoder has achieved reduction of 18.75 % in area, 44.15 % in terms of cell count, and 16.5 % in total energy dissipation when compared to reference encoder. In terms of QCA cost, reduction of 12.5 % is achieved in case of proposed structures. The energy dissipated in the proposed designs is less compared to reference encoder. Proposed-2 structure is more efficient compared to multilayer and reference encoder in terms of cell count, cell area and QCA cost. The QCA circuits are realized in QCADesigner and analyzed energy in QCADesigner-E. [ABSTRACT FROM AUTHOR]

In this article, we use group action theory to define some important ternary linear codes. Some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. Then, we define two new codes sharing the same automorphism group isomorphic to $C_2 \times M_{11}$ where $M_{11}$ is the Sporadic Mathieu group and $C_{2}$ is a cyclic group of two elements. We also study the natural action of the general linear group $GL (k, 2) $ on the vector space $F_2 ^ k$ to characterize Hamming codes $H_k (2) $ and their automorphism group.

This paper studies linear and affine error-correcting codes for correcting synchronization errors such as insertions and deletions. We call such codes linear/affine insdel codes. Linear codes that can correct even a single deletion are limited to having an information rate at most 1/2 (achieved by the trivial two fold repetition code). Previously, it was (erroneously) reported that more generally no nontrivial linear codes correcting k deletions exist, i.e., that the (k + 1)-fold repetition codes and its rate of 1/(k + 1) are basically optimal for any k. We disprove this and show the existence of binary linear codes of length n and rate just below 1/2 capable of correcting \Omega(n) insertions and deletions. This identifies rate 1/2 as a sharp threshold for recovery from deletions for linear codes and reopens the quest for a better understanding of the capabilities of linear codes for correcting insertions/deletions. We prove novel outer bounds and existential inner bounds for the rate vs. (edit) distance trade-off of linear insdel codes. We complement our existential results with an efficient synchronization-string-based transformation that converts any asymptotically good linear code for Hamming errors into an asymptotically good linear code for insdel errors. Last, we show that the 2 -rate limitation does not hold for affine codes by giving an explicit affine code of rate 1 - e epsilon which can efficiently correct a constant fraction of insdel errors. [ABSTRACT FROM AUTHOR]

Error-correcting output coding (ECOC) is a method for constructing a multi-valued classifier using a combination of given binary classifiers. ECOC can estimate the correct category by other binary classifiers even if the output of some binary classifiers is incorrect based on the framework of the coding theory. The code word table representing the combination of these binary classifiers is important in ECOC. ECOC is known to perform well experimentally on real data. However, the complexity of the classification problem makes it difficult to analyze the classification performance in detail. For this reason, theoretical analysis of ECOC has not been conducted. In this study, if a binary classifier outputs the estimated posterior probability with errors, then this binary classifier is said to be noisy. In contrast, if a binary classifier outputs the true posterior probability, then this binary classifier is said to be noiseless. For a theoretical analysis of ECOC, we discuss the optimality for the code word table with noiseless binary classifiers and the error rate for one with noisy binary classifiers. This evaluation result shows that the Hamming distance of the code word table is an important indicator. [ABSTRACT FROM AUTHOR]

In this paper we investigate some dual algebraic-geometric codes associated with the Giulietti–Korchmáros maximal curve. We compute the minimum distance and the minimum weight codewords of such codes and we investigate the generalized Hamming weights of such codes. [ABSTRACT FROM AUTHOR]

Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory on the minimum locality of linear codes. In addition, the minimum locality of many known families of linear codes has not been studied in the literature. Motivated by these two facts, this paper develops some general theory about the minimum locality of linear codes, and investigates the minimum locality of a number of families of linear codes, such as q-ary Hamming codes, q-ary Simplex codes, generalized Reed-Muller codes, ovoid codes, maximum arc codes, the extended hyperoval codes, and near MDS codes. Many classes of both distance-optimal and dimension-optimal LRCs are presented in this paper. To this end, the concepts of linear locality and minimum linear locality are specified. The minimum linear locality of many families of linear codes are settled with the general theory developed in this paper. [ABSTRACT FROM AUTHOR]

Convolutional codes form an important class of codes that have memory. One natural way to study these codes is by means of input state output representations. In this paper we study the minimum (Hamming) weight among codewords produced by input sequences of weight two. In this paper, we consider rate 1=n and use the linear system setting called (A; B;C; D) input-state-space representations of convolutional codes for our analysis. Previous results on this area were recently derived assuming that the matrix A, in the input-state-output representation, is nonsingular. This work completes this thread of research by treating the nontrivial case in which A is singular. Codewords generated by weight-2 inputs are relevant to determine the effective free distance of Turbo codes. [ABSTRACT FROM AUTHOR]

This paper revisits a combinatorial structure called the large set of ordered design ( L O D ). Among others, we introduce a novel structure called Latin matching and prove that a Latin matching of order n leads to an L O D (n − 1 ,   n ,   2 n − 1) ; thus, we obtain constructions for L O D (1 ,   2 ,   3) , L O D (2 ,   3 ,   5) , and L O D (4 ,   5 ,   9) . Moreover, we show that constructing a Latin matching of order n is at least as hard as constructing a Steiner system S (n − 2 ,   n − 1 ,   2 n − 2) ; therefore, the order of a Latin matching must be prime. We also show some applications in multiagent systems. [ABSTRACT FROM AUTHOR]

In this article, we use group action theory to define some important ternary linear codes. Some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. Then, we define two new codes sharing the same automorphism group isomorphic to C2xM11 where M11 is the Sporadic Mathieu group and C2 is a cyclic group of two elements. We also study the natural action of the general linear group GL(k,2) on the vector space F2k to characterize Hamming codes Hk(2) and their automorphism group. [ABSTRACT FROM AUTHOR]

Steganography is the science of communicating a secret message by hiding it in a cover object. The well known F5 algorithm is based on binary Hamming codes in Hamming graph. It has been an interesting research problem to construct other steganographic schemes from mathematically structured graphs. In this paper, we construct steganographic schemes explicitly from r-perfect codes on Cayley graphs over Gaussian integers, Eisenstein–Jacobi integers, and Lipschitz integers, respectively. Then we further compute various parameters for the suggested steganographic schemes. [ABSTRACT FROM AUTHOR]

Advances in integrated circuit production technologies have reduced device sizes, leading to corresponding scaling in electrical characteristics, such as threshold voltage. This scaling has increased the susceptibility of devices to electromagnetic radiation, raising the bitflip probability. Systems requiring a certain level of fault tolerance employ techniques like Error Correction Codes (ECC), providing a degree of reliability in mitigating this issue. The error correction and detection efficacies and ECC scalability vary based on the encoding and codestruct employed. This study employs four Hamming and parity code organizations for performing four Two-Dimensional (2D)-ECCs (N × 4p, N × ExHam, N × Ham_p, and N × Ham2_2p). We investigated the scalability, synthesis results, and correction and detection rates employing the same number of check and data bits for the four 2D-ECCs. The results point to the advantages for ECCs that employ cross-checking using radiation-hardened memories for checkbits, especially when ECCs scale to large codestructs. • Investigate four 2D-ECC organizations (N × 4p, N × ExHam, N × Ham_p, N × Ham2_2p) • Compared correction/detection, synthesis costs, and scalability of proposed 2D-ECCs • Address device susceptibility to radiation, emphasizing ECCs for fault tolerance • Explore the performance impact of coding schemes and organizational structures [ABSTRACT FROM AUTHOR]