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Quick Response (QR) code, a machine-readable symbol, is widely employed in all walks of life due to its large information capacity, strong error correction ability, and fast reading speed. However, anyone with a standard decoder could obtain stored information. In this paper, utilizing the characteristics of the Hamming code, wet paper code, and the recognition mechanism of the QR code, we introduce a high-capacity QR code with three-layer information to protect the sensitive information. In the proposed scheme, we utilize the XOR-based secret-sharing algorithm to embed the second-layer information on the column vector of the constructed random matrix block. Then, without affecting the embedding result of the second layer information, the matrix block elements are reused again, and the Hamming code is constructed with the column vector. Based on the error correction mechanism of the Hamming code, the third layer of information is embedded on the column vector and encoded by wet paper coding to realize the blind extraction. Finally, based on the recognition mechanism of the QR code, the random matrix block containing the secret information is fused with the carrier QR code, and the public information of the carrier QR code is used as the first-layer information. Compared with other schemes, the proposed scheme has the advantages of high information payload, low computational complexity, and strong robustness. [ABSTRACT FROM AUTHOR]

Advances in structural biology of aminoacyl-tRNA synthetases (aaRSs) have revealed incredible diversity in how aaRSs bind their tRNA substrates. The causes of this diversity remain mysterious. We developed a new class of highly rugged fitness landscape models called match landscapes, through which genes encode the assortative interactions of their gene products through the complementarity and identifiability of their structural features. We used results from coding theory to prove bounds and equalities on fitness in match landscapes assuming additive interaction energies, macroscopic aminoacylation kinetics including proofreading, site-specific modifiers of interaction, and selection for translational accuracy in multiple, perfectly encoded site-types. Using genotypes based on extended Hamming codes we show that over a wide array of interface sizes and numbers of encoded cognate pairs, selection for translational accuracy alone is insufficient to displace the tRNA-binding interfaces of aaRSs. Yet, under combined selection for translational accuracy and rate, site-specific modifiers are selected to adaptively displace the tRNA-binding interfaces of non-cognate aaRS–tRNA pairs. We describe a remarkable correspondence between the lengths of perfect RNA (quaternary) codes and the modal sizes of small non-coding RNA families. [ABSTRACT FROM AUTHOR]

A common way to protect data stored in DRAM and related memory systems is through the use of an error-correcting code such as the extended Hamming code. Traditionally, these error-correcting codes provide equal protection guarantees to all messages. In this paper, we focus on unequal message protection (UMP), in which a subset of messages is deemed as special, and is afforded additional error-correction protection while maintaining the same number of redundancy bits as the baseline code. UMP is a powerful approach when the special messages are chosen based on the knowledge of data patterns in context. Our objective is to construct deterministic, algebraic codes with guaranteed UMP properties, derive their cardinality bounds using novel combinatorial techniques, and to demonstrate their efficacy for realistic memory benchmarks. We first introduce a UMP alternative to the single-bit parity-check code, and then we generalize to a broader UMP code family, including a UMP alternative to the extended Hamming code, offering full double-error correction protection to special messages. Our UMP constructions, applied to main memory in high-performance computing applications, could lead to significant system-level benefits such as less frequent checkpoints in supercomputers and decreased risk of catastrophic failure from erroneous special messages. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to give a new and general way to obtain steganographic schemes from perfect codes on Cayley graphs, motivated by the F5 algorithm based on binary Hamming codes. We obtain the steganography based on perfect Hamming codes as a special case and also give various equivalent conditions for the existence of a perfect code on a k-regular Abelian Cayley graph. Then we show that a perfect code on an Abelian Cayley graph produces a proper steganographic scheme. We further compute the various parameters for the steganographic scheme of type [n, k] over a finite field F q arising from a linear [n, n − k, d] code over F q and find also parameters for some steganographic schemes from perfect codes in k-regular Abelian Cayley graphs. [ABSTRACT FROM AUTHOR]

Error control codes (ECC) play an important role in the detection and correction of data errors over unreliable or noisy communication channels. The main idea of ECC is to add redundant bits to the message on the transmitter, which can be used to detect and correct certain errors on the receiver. ECC are used in numerous applications such as telecommunications, Internet, and data storage. Different types of ECC exist such as linear block, convolutional, and turbo codes. This paper presents results from an innovative undergraduate research project involving implementation of linear block, cyclic and convolutional codes in very high speed integrated circuit hardware description language (VHDL) using a field‐programmable gate array (FPGA). FPGA is a suitable platform for implementing ECC due to the advantages of performance, time to market, cost, reliability, and long‐term maintenance. As part of this project, (7,4) Hamming code used for linear block and cyclic codes and convolutional codes with constraint length k of 3 and code rate (k/n) of 1/2 were implemented in VHDL on a Xilinx Spartan‐6 FPGA using ISE 14.7. Two undergraduate students at Purdue University Northwest worked on this project. This was the students' first exposure to ECC, VHDL, and FPGA, as undergraduate students are usually not introduced to these topics in traditional electrical and computer engineering curriculum. The goal of this project was to provide students with hands‐on experience using industry‐standard VHDL software and FPGA hardware platforms to implement ECC. This paper presents the results of this innovative project including register‐transfer level schematics, simulations, and VHDL code for encoders and decoders for the various ECC implemented, and students' reflections on the project. [ABSTRACT FROM AUTHOR]

Linear block code (LBC) is an error detection and correction code that is widely used in communication systems. In this paper a special type of LBC called Hamming code was implemented and debugged using FPGA kit with integrated software environments ISE for simulation and tests the results of the hardware system. The implemented system has the ability to correct single bit error and detect two bits error. The data segments length was considered to give high reliability to the system and make an aggregation between the speed of processing and the hardware ability to be implemented. An adaptive length of input data has been consider, up to 248 bits of information can be handled using Spartan 3E500 with 43% as a maximum slices utilization. Input/output data buses in FPGA have been customized to meet the requirements where 34% of input/output resources have been used as maximum ratio. The overall hardware design can be considerable to give an optimum hardware size for the suitable information rate. [ABSTRACT FROM AUTHOR]

Recently, Etzion et al. introduced metrics on ${\mathbb{F}}_{2}^{n}$ based on directed graphs on $n$ vertices and developed some basic coding theory on directed graph metric spaces. In this paper, we consider the problem of classifying directed graphs, which admit the extended Hamming codes to be a perfect code. We first consider weighted poset metrics as a natural generalization of poset metrics and investigate interrelation between the weighted poset metrics and the directed graph-based metrics. In the next, we classify weighted posets on a set with eight elements and directed graphs on eight vertices, which admit the extended Hamming code $\tilde {\mathcal {H }}_{3}$ to be a two-perfect code. We also construct some families of such structures for any $k \geq 3$ , which can be viewed as generalizations of some results presented by Etzion et al. and Hyun and Kim. Those families enable us to construct packing or covering codes of radius 2 under certain maps. [ABSTRACT FROM AUTHOR]

Palmprint contains stable and effective features, especially the orientation and scale features of palm lines, and has now become an important identity recognition technique for surveillance and safety applications. Existing palmprint recognition methods using texture features can be roughly divided into two categories: coding-based and local descriptor based methods. As compared with the latter category, the former one can make full use of the palmprint specific features and acquire fast matching speed. However, most existing coding-based methods are based on the competitive coding scheme, in which the scale features of palmprint cannot be well exploited. In this work, we propose a discriminant orientation and scale features learning (DOSFL) for palmprint recognition. By introducing the idea of discriminant analysis into palmprint coding, DOSFL can extract the orientation and scale features with more favorable discriminability. Then, DOSFL utilizes four code bits to represent both the orientation and scale features of palmprint, and employs the Hamming distance for code matching. To make better use of the orientation and scale information contained in palmprint samples, we further propose a multi-orientation and multi-scale features discriminant learning (MOSDL) approach for palmprint recognition, which can fuse different orientation and scale feature information effectively in the discriminant learning process. Experimental results on two publicly available palmprint databases, including the HK PolyU database and UST palmprint image database, demonstrate that our proposed approach can achieve better recognition results than the compared methods. [ABSTRACT FROM AUTHOR]

This work presents an electro-optic effect-based design for the widely used Hamming code for checking single bit errors in the received data. The structure is based on Mach-Zehnder Interferometer, designed using Titanium-diffused Lithium Niobate-based waveguides. The proposed device has been successfully tested using the beam propagation method. For a received 7-bit code, the three simultaneously generated check bits are combined to check the error position. Critical performance parameters like extinction ratio (24.39dB), contrast ratio (25.711dB), insertion loss (0.041dB), and amplitude modulation (0.079dB) calculated for the overall device are within acceptable limits for the feasibility of the device. [ABSTRACT FROM AUTHOR]

Grassmannian codes are known to be useful in error correction for random network coding. Recently, they were used to prove that vector network codes outperform scalar linear network codes, on multicast networks, with respect to the alphabet size. The multicast networks which were used for this purpose are generalized combination networks. In both the scalar and the vector network coding solutions, the subspace distance is used as the distance measure for the codes which solve the network coding problem in the generalized combination networks. In this paper, we show that the subspace distance can be replaced with two other possible distance measures which generalize the subspace distance. These two distance measures are shown to be equivalent under an orthogonal transformation. It is proved that the Grassmannian codes with the new distance measures generalize the Grassmannian codes with the subspace distance and the subspace designs with the strength of the design. Furthermore, optimal Grassmannian codes with the new distance measures have minimal requirements for the network coding solutions of some generalized combination networks. The coding problems related to these two distance measures, especially with respect to network coding, are discussed. Finally, by using these new concepts, it is proved that the codes in the Hamming scheme form a subfamily of the Grassmannian codes. [ABSTRACT FROM AUTHOR]

Hamming code is a linear error-correcting code widely used in memory and telecommunication. For the first time, here we put forth an approach to analyzing Hamming codes in hardware using networks consisting of memristors. Such networks are capable of detecting and correcting potential bit errors in Hamming codes in a high-speed and energy-efficient way, where the parity-check matrix is stored in the memristor crossbar array and the syndrome vector is represented by the states of the output unipolar memristors whose resistance flipping naturally implements vector-matrix multiplication with modulo 2. Our experimental results demonstrate that the output syndrome vector is able to correctly represent the position of the bit error whenever it exists, and subsequent correction can thus be applied by flipping the bit identified. The energy consumption using the present network has decreased by >100 times compared with GPU while >1000 times compared with CPU. [ABSTRACT FROM AUTHOR]

Recently, Jana et al. proposed the partial reversible data hiding (PRDH) based on (7, 4) Hamming code, which deals with three images: the original image (OI), the cover image (CI), and the stego image (SI). The CI is obtained by slightly modifying OI. After that, one can embed secret into CI to generate SI. The so-called partial reversible feature is that we can reconstruct the CI faultlessly, which is almost the same to the OI. However, in Jana et al.'s PRDH, the authors only adjust redundant bits by using (7, 4) Hamming code with even (or odd) parity. This simple approach may modify 3 redundant bits at most in 7 least significant bit (LSBs) to obtain CI from OI, and this degrades the CI quality seriously. In this paper, we construct two schemes: the proposed PRDH (PPRDH) and the modified PRDH (MPRDH). PPRDH enhances the partial reversible property that improves the visual quality of CI. And, MPRDH enhances PPRDH to achieve the high embedding capacity. Theoretical estimations of average mean square errors for these PRDH schemes are given to demonstrate the advantage of our PRDH schemes. In addition, we also point out two inaccurate descriptions in Jana et al.'s PRDH about position of embedded secret to more simplify the procedure of embedding secret. [ABSTRACT FROM AUTHOR]

Matrix coding based data hiding (MCDH) using linear codes (syndrome coding) is an efficient coding method for steganographic schemes to improve their embedding efficiency. Hamming code data hiding (HDH) is a well-known MCDH using a covering function COV (1, n = 2k − 1, k). Afterwards, Hamming+ 1 DH (H1DH) was proposed with good embedding efficiency. However, these two previous approaches, HDH and H1DH, are not efficient for a large amount of messages. To tackle this problem, Yang et al.'s proposed Hamming+ k DH (Hk DH), which enhance the extra one embedded bit in H1DH to k embedded bits in the Hk DH. In this paper, we extended the Hk DH to the Hamming+ k with m overlapped pixels (Hk_mDH). The proposed Hk_mDH adopted pixel overlapping approach, optimal pixel adjustment process (OPAP), and Least Significant Bit (LSB) substitution. Experimental results demonstrate that our Hk_mDH has better embedding rate (ER) compared with previous schemes. In addition, we have proved that our Hk_mDH has excellent theoretical estimation of average mean square error. [ABSTRACT FROM AUTHOR]

Various studies have been conducted on a secret key exchange using the inter-pulse interval (IPI) extracted from a pulse wave. The IPI-based key exchange method uses a point where the body can measure an IPI of similar value anywhere. The IPI measured to generate the secret key shares the error correction code between biometric sensors and generates the key using the corrected IPI. Peak misdetection negatively affects key generation because the IPI does not consistently match. In this paper, we propose a method to detect misdetection and recover IPI using thresholds. The proposed method reduces the cost of communication compared to the previous method, which is not only energy efficient but also key generating. The efficiency of the recovery method is also demonstrated. Tests results show the total number of IPI recoveries is 19, while the key generation rate is 99.4%. [ABSTRACT FROM AUTHOR]

The hull of linear codes has promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed–Solomon codes and extended generalized Reed–Solomon codes over finite fields with respect to the Euclidean inner product. Several infinite families of MDS codes with hulls of arbitrary dimensions are presented. As an application, using these MDS codes with hulls of arbitrary dimensions, we construct several new infinite families of entanglement-assisted quantum error-correcting codes with flexible parameters. [ABSTRACT FROM AUTHOR]

We study array codes which are based on subspaces of a linear space over a finite field, using spreads, $q$ -Steiner systems, and subspace transversal designs. We present several constructions of such codes which are $q$ -analogs of some known block codes, such as the Hamming and simplex codes. We examine the locality and availability of the constructed codes. In particular, we distinguish between two types of locality and availability: node versus symbol. The resulting codes have distinct symbol/node locality/availability, allowing a more efficient repair process for a single symbol stored in a storage node of a distributed storage system, compared with the repair process for the whole node. [ABSTRACT FROM AUTHOR]

The paper deals with perfect 1-error correcting codes over a finite field with q elements (briefly q-ary 1-perfect codes). We show that the orthogonal code to a q-ary non-full-rank 1-perfect code of length n = (q m - 1) / (q - 1) is a q-ary constant-weight code with Hamming weight equal to q m - 1 , where m is any natural number not less than two. Necessary and sufficient conditions for q-ary codes to be q-ary non-full-rank 1-perfect codes are obtained. We suggest a generalization of the concatenation construction to the q-ary case and construct a ternary 1-perfect code of length 13 and rank 12. [ABSTRACT FROM AUTHOR]

A ${\mathbb {Z}}_{2}{\mathbb {Z}}_{4}$ -additive code ${\mathcal{ C}}\subseteq {\mathbb {Z}}_{2}^\alpha \times {\mathbb {Z}}_{4}^\beta $ is called cyclic if the set of coordinates can be partitioned into two subsets, the set of ${\mathbb {Z}}_{2}$ coordinates and the set of ${\mathbb {Z}}_{4}$ coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. Let $\Phi ({\mathcal{ C}})$ be the binary Gray map image of ${\mathcal{ C}}$. We study the rank and the dimension of the kernel of a ${\mathbb {Z}}_{2} {\mathbb {Z}}_{4} $ -additive cyclic code ${\mathcal{ C}}$ , that is, the dimensions of the binary linear codes $\langle \Phi ({\mathcal{ C}}) \rangle $ and $\ker (\Phi ({\mathcal{ C}}))$. We give upper and lower bounds for these parameters. It is known that the codes $\langle \Phi ({\mathcal{ C}}) \rangle $ and $\ker (\Phi ({\mathcal{ C}}))$ are binary images of ${\mathbb {Z}}_{2} {\mathbb {Z}}_{4}$ -additive codes that we denote by ${\mathcal{ R}}({\mathcal{ C}})$ and ${\mathcal{ K}}({\mathcal{ C}})$ , respectively. Moreover, we show that ${\mathcal{ R}}({\mathcal{ C}})$ and ${\mathcal{ K}}({\mathcal{ C}})$ are also cyclic and determine the generator polynomials of these codes in terms of the generator polynomials of the code ${\mathcal{ C}}$. [ABSTRACT FROM AUTHOR]

We study about monotonicity of r -identifying codes in binary Hamming space, q-ary Lee space and incomplete hypercube. Also, we give the lower bounds for M 1 , q (≤ l) (n) where M 1 , q (≤ l) (n) is the smallest cardinality among all r -identifying codes in ℤ q n with respect to the Lee metric. We prove the existence of 1 -identifying code in an incomplete hypercube. Also, we give the construction techniques for r -identifying codes in the incomplete hypercubes in Secs. 4.1 and 4.2. Using these techniques, we give the tables (see Tables 1–6) of upper bounds for M I H , r (k) where M I H , r (k) is the smallest cardinality among all r -identifying codes in an incomplete hypercube with k processors. Also, we give the exact values of M I H , r (k) for small values of r and k (see Sec. 4.3). [ABSTRACT FROM AUTHOR]

A robust H.264/AVC video watermarking algorithm without intra distortion drift is proposed in this paper for the copyright protection of digital videos. The classic scheme prevented distortion from drifting by the classification of intra prediction modes, and different categories have different methods for modifying coefficient-pairs. Based on the reference pixels when 4 × 4 blocks of videos are encoded, the improved scheme proposed in this paper introduces a reclassification of intra prediction modes into avoiding distortion drift, which efficient enlarges the capacity of this kind of methods. Besides, the chosen principle of coefficient-pairs for watermarking is presented by theoretical and experimental analysis. By the means above, watermarked videos have controlled bit rate growth and guaranteed visual quality even if the capacity is enlarged. Then, pre-processing of watermarks reasonable reduce the bits needed to embed, which fixes the problem in classic scheme about limited capacity limits the size of watermarks. Meanwhile, spread-spectrum and Hamming code employed together not only promote robustness but also reduce computational complexity. Experimental results show that compared with the classic robust distortion drift-free methods, our algorithm maintains good visual performance with the enlarged capacity, and the strong robustness is kept without a huge increasement of bit rate. [ABSTRACT FROM AUTHOR]

Additional check bits, which are commonly attached to the message’s input data, are normally used to minimize the error during data transmission. The receiver system implements a checking algorithm to determine if an error was occurred in the received data. This algorithm will correct a corrupted bit and recover the original message. An enhanced error detection correction code was presented to better detect and correct the corrupted conveyed bits. It improves the existing limitations of utilizing cyclic redundancy checking (CRC), Hamming code, and other checksum techniques. Also, it reduced the length of the redundancy bits which exists in CRC, the overhead of interspersing of the redundancy bits in a typical Hamming code, and the system resources such as processor time and bandwidth in checksum techniques. This paper was synthesized and simulated using the Xilinx Spartan 6 (XC7Z020-2CLG4841) FPGA. Results show that the resource utilization of the designed memory architecture using EEDC is lower compared to CRC, Hamming, and Checksum algorithms. [ABSTRACT FROM AUTHOR]

We study eigenfunctions and perfect colorings of the n-dimensional q-ary Hamming graph. We obtain the formulae of interdependence of local distributions for an eigenfunction in two orthogonal faces. We prove an analogous result for perfect colorings. [ABSTRACT FROM AUTHOR]

The field of nanosatellites is constantly evolving and growing at a very fast speed. This creates a growing demand for more advanced and reliable EDAC systems that are capable of protecting all memory aspects of satellites. The Hamming code was identified as a suitable EDAC scheme for the prevention of single event effects on-board a nanosatellite in LEO. In this paper, three variations of Hamming codes are tested both in Matlab and VHDL. The most effective version was Hamming [16, 11, 4]2. This code guarantees single-error correction and double-error detection. All developed Hamming codes are suited for FPGA implementation, for which they are tested thoroughly using simulation software and optimized. [ABSTRACT FROM AUTHOR]

Multiple cell upsets (MCU) is an issue that has to be dealt with when designing electronics for working in a radiated environment. Furthermore, the constant evolution of ICs integration density causes an increment in the MCUs span. These issues are typical in aviation applications, where, additionally, fault-tolerant (FT) performance is required. FT systems are typically based on a redundancy concept for storing and retrieving healthy information, for example, with a triple modular redundancy (TMR) scheme. The main issue with redundancy is design oversizing. On the other hand, reconfiguration-based techniques allow error scrubbing with a limited overhead. The main drawback here is overhead vulnerability to radiation, which is invalid for FT requirements. This paper proposes a new hybrid architecture that takes advantage of the optimized performance of reconfiguration-based techniques supported on extremely compressed redundant information nonvulnerable to radiation, referred to in this paper as hardwired seed bits (HSB). It also includes different known techniques, such as interleaving, error detection and correction (EDAC) algorithms, etc., for optimizing the final architecture as much as possible. As a result, the proposed approach meets FT requirements thanks to nonvulnerable tiny redundant information combined with an optimized performance through EDAC-based implementation. [ABSTRACT FROM AUTHOR]

Radiation effects in star trackers can cause malfunctions that may lead to the loss of communication with the satellite. This paper presents a scheme to protect star tracker images stored in memory against single event upsets (SEUs). Fault injection and resource utilization reports show that, with the protection technique, 99.98% of the SEUs can be corrected using 37% less memory space than single error correction Hamming codes. The remaining 0.02% has a negligible effect in the star identification algorithm. [ABSTRACT FROM AUTHOR]

Using the method for constructing binary self-dual codes with an automorphism of order square of a prime number, we have classified all binary self-dual codes with length 76 having minimum weight $d=14$ via automorphism of order 9. Up to equivalence, there are six self-dual [76, 38, 14] codes with an automorphism of type 9-(8, 0, 4). All codes obtained have new values of the parameter in their weight enumerator, thus more than doubling the number of known values. [ABSTRACT FROM AUTHOR]

Abstract Inspired by code vertex operator algebras (VOAs) and their representation theory, we define code algebras, a new class of commutative non-associative algebras constructed from binary linear codes. Let C be a binary linear code of length n. A basis for the code algebra A C consists of n idempotents and a vector for each non-constant codeword of C. We show that code algebras are almost always simple and, under mild conditions on their structure constants, admit an associating bilinear form. We determine the Peirce decomposition and the fusion law for the idempotents in the basis, and we give a construction to find additional idempotents, called the s -map, which comes from the code structure. For a general code algebra, we classify the eigenvalues and eigenvectors of the smallest examples of the s -map construction, and hence show that certain code algebras are axial algebras. We give some examples, including that for a Hamming code H 8 where the code algebra A H 8 is an axial algebra and embeds in the code VOA V H 8 . [ABSTRACT FROM AUTHOR]

Highlights • A binary hash codes learning algorithm for finger vein image retrieval is proposed. • A finger vein image representation method called NSC is proposed. • The results show the effectiveness and efficiency of our proposed method. Abstract High dimensional real-valued features have been shown to be effective for finger vein identification, but result in high computational cost especially in a large-scale finger vein database. Therefore compact binary codes are generally used to obtain fast query speed as well as reduce storage requirements. However, only a few strategies are available for finger vein retrieval in Hamming space, and existing binary representation of finger veins can become unstable and undiscriminating due to finger vein variations induced by translation, rotation and illumination. In this paper, we propose a binary hash codes learning algorithm to map finger vein images in the original feature space to Hamming space. First, to obtain the discriminative finger vein image features, a novel finger vein image representation method called Nonlinearly Subspace Coding (NSC) is proposed. The codebook is a union of low-dimensional linear subspaces instead of visual words. For a given local finger vein texton, its top-k nearest subspaces are found and the texton is nonlinearly mapped into these subspaces. Then, a finger vein Binary Hash Codes (BHC) learning method is proposed by jointly considering the discriminability and the stability of the binary code. Experimental results on a two-session public finger vein database and a large fused finger vein database demonstrate the effectiveness and efficiency of our binary hash coding learning algorithm for large-scale finger vein retrieval. [ABSTRACT FROM AUTHOR]

This paper is a short survey of projective geometry, history of Hamming codes and the relationship between them and projective planes. The projective plane of order n, over a finite field (Fp ={0,1,2,..., p -1},+,*) p, which has arithmetic donemod p, denoted by PG(n, p), is the set of all subspaces of vector space Fnp. It can be endowed with the distance function f (U,V) = dim(U)+ dim(V) - 2dim(U V) which turns PGn, p into a metric space. A (n,M,d) code in projective space is a subset of PG(n, p) of size M such that the distance between any two code-words is at least d. The first error correction code, the Hamming code, is intrinsic to the projective plane of order 2 over F2 . A connection between planes and codes is given by construction of Hamming code related to PG(2,2) and we generalize them to PG(3,2) using Hamming and Generator matrix. The codes constructed in this way are called projective codes. [ABSTRACT FROM AUTHOR]

Highlights • We proposed new separable reversible data hiding based on halftoned images. • Our proposed scheme improves the embedding efficiency using Hamming code. • Our proposed scheme is the first scheme to deal with the halftoned image. Abstract In this paper, new high-capacity separable reversible data hiding in an encrypted halftoned image is proposed. The proposed scheme used Hamming code to exploit embedding efficiency with a halftoned image. Our proposed scheme is meeting a condition of separable reversible data hiding in the encrypted image (SRDHEI) and can achieve a high embedding efficiency of a halftoned image with low distortion. Experimental results also show that the scheme provides a large embedding payload and reconstructs about the same original halftoned image and embedded additional information. [ABSTRACT FROM AUTHOR]

We construct two series of linear codes C(G) over Fq[x]/(x2) and GR(p2,m) reaching the Griesmer bound. Moreover, we consider the Gray images of C(G). The results show that the Gray images of C(G) over Fq[x]/(x2) are linear and also reach the Griesmer bound in some cases, and many of linear codes over Fq we constructed have two Hamming (non-zero) weights. [ABSTRACT FROM AUTHOR]

Deploying a cylindrical heaving wave energy converter (WEC) in front of a parabolic breakwater forms a basic module for synergetic coast protection and power generation. The interactions in the hybrid system are important to its performance but poorly understood. Here the power amplification effect of the parabolic breakwater on the WEC and the additional wave attenuation effect of the WEC on the parabolic breakwater are investigated based on the potential flow theory of linear regular waves. A parabolic breakwater and five WECs with optimized geometry and generator parameters are employed in comparative numerical studies conducted using an open-source code HAMS. Results show that the parabolic breakwater has similar power amplification effects on different WECs, despite the significant differences in their dimensions and power-take-off damping. The power of a WEC can be increased by more than 120% at its natural period. A WEC can shadow the region behind it and reduce the wave amplitude on the opening wall of the parabolic breakwater. It also slightly reduces the amplitude of the relatively high waves in the protection zone behind the breakwater. A flatter WEC with a larger diameter-to-draft ratio is recommended as it generates more power and has a stronger shadow effect. • A novel breakwater-WEC hybrid system is proposed and optimized. • The system involves a heaving cylindrical WEC in front of a parabolic breakwater. • The overall power generation and wave attenuation performance is investigated. • The interactions between the breakwater and the WEC are analysed. • Recommendations for the WEC geometry are provided. [ABSTRACT FROM AUTHOR]

Communication links forming secure telecommunications networks rely on various technologies such as message switching, circuit switching, or packet switching to transmit messages and data. Hamming codes, a family of linear error-correcting codes, are commonly used in communication networks to detect and correct one-bit and two-bit errors. However, reducing power consumption, occupied area, and latency in secure telecommunication networks remains a challenge for future information and communication technology. To address these challenges, emerging technologies like quantum dots offer potential solutions. Quantum-dot cellular automata (QCA) stands as a promising frontier in nanotechnology for enhancing secure telecommunications networks. It opens up the possibility of crafting high-performance, energy-efficient digital circuits. This research harnesses the potential of QCA and introduces groundbreaking innovations: a 3-8 decoder employing a single-layer layout and a 3-input XOR gate with a multi-layer configuration. These components are utilized in the design of an electronic circuit for Hamming codes, incorporating the QCA-based approach. It is important to note that practical implementation in real-world scenarios presents challenges due to the nature of QCA technology. As a result, the evaluation and validation of the proposed designs heavily rely on simulations using QCADesigner. While experimental validation in real-world scenarios is limited, the simulations provide insights into the functionality and feasibility of the suggested designs. By leveraging QCA, the proposed Hamming code circuit significantly enhances cell count, occupied area, and clock latency. The suggested design can be adapted to fit different generating matrices in Hamming codes without requiring drastic modifications to the underlying architecture. [ABSTRACT FROM AUTHOR]

In this paper, we describe a correspondence between a fuzzy linear code and a family of nested linear codes. We also describe the arithmetic of fuzzy linear codes. As a special class of nested linear codes, we consider a family of nested self-orthogonal codes. A linear code is self-orthogonal if it is contained in its dual and self-dual if it is equal to its dual. We introduce a definition of fuzzy self-dual or self-orthogonal codes which include classical self-dual or self-orthogonal codes. As examples, we construct several interesting classes of fuzzy linear codes including fuzzy Hamming codes, fuzzy Golay codes, and fuzzy Reed-Muller codes. We also give a general decoding algorithm for fuzzy linear codes. [ABSTRACT FROM AUTHOR]

A double Hamming distance‐based 2D reordering method is proposed for a test set with don't care bits (Xs) to reduce scan‐in power and compress test patterns. In this method, the rows and columns in the test set are reordered sequentially so that similar rows or columns are aggregated together. Being different from other reordering‐based methods, the authors' method reorders every two rows or columns with more identical bits closer in the whole reordering process, where more Xs are clustered. Each X is then replaced with 0 or 1 using minimum transition filling scheme to minimise '1‐0' and '0‐1' logical state transitions. A small number of the logic state transitions cause low switching activity, which not only reduces scan‐in power consumption but also facilitates code‐based test pattern compression. Experimental results show that their proposed method achieves peak and average power reductions of 18.01 and 12.97% compared to the state‐of‐the‐art method, respectively. Furthermore, the compression ratio of alternating shifted frequency directed run‐length coding is improved to 73.76% in average utilising their proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we study deep holes of Gabidulin codes in both rank and Hamming metrics. Specifically, first, we give a tight lower bound for the distance of any word to a Gabidulin code and a sufficient and necessary condition for achieving this lower bound as well. Then, a class of deep holes of a Gabidulin code are discovered. Furthermore, we obtain some other deep holes for certain Gabidulin codes. [ABSTRACT FROM AUTHOR]

Abstract It is known that the binary generalized Goppa codes are perfect codes for the weighted Hamming metrics. In this paper, we present the existence of a weighted Hamming metric that admits a binary Hamming code (resp. an extended binary Hamming code) to be perfect code. For a special weighted Hamming metric, we also give some structures of a 2-perfect code, show how to construct a 2-perfect linear code and obtain the weight distribution of a 2-perfect code from the partial information of the code. [ABSTRACT FROM AUTHOR]

Currently, faults suffered by SRAM memory systems have increased due to the aggressive CMOS integration density. Thus, the probability of occurrence of single-cell upsets (SCUs) or multiple-cell upsets (MCUs) augments. One of the main causes of MCUs in space applications is cosmic radiation. A common solution is the use of error correction codes (ECCs). Nevertheless, when using ECCs in space applications, they must achieve a good balance between error coverage and redundancy, and their encoding/decoding circuits must be efficient in terms of area, power, and delay. Different codes have been proposed to tolerate MCUs. For instance, Matrix codes use Hamming codes and parity checks in a bi-dimensional layout to correct and detect some patterns of MCUs. Recently presented, column–line–code (CLC) has been designed to tolerate MCUs in space applications. CLC is a modified Matrix code, based on extended Hamming codes and parity checks. Nevertheless, a common property of these codes is the high redundancy introduced. In this paper, we present a series of new low-redundant ECCs able to correct MCUs with reduced area, power, and delay overheads. Also, these new codes maintain, or even improve, memory error coverage with respect to Matrix and CLC codes. [ABSTRACT FROM AUTHOR]

The maximum independent sets in the Doob graphs D(m, n) are analogs of the distance-2 MDS codes in Hamming graphs and of the latin hypercubes. We prove the characterization of these sets stating that every such set is semilinear or reducible. As related objects, we study vertex sets with maximum cut (edge boundary) in D(m, n) and prove some facts on their structure. We show that the considered two classes (the maximum independent sets and the maximum-cut sets) can be defined as classes of completely regular sets with specified 2-by-2 quotient matrices. It is notable that for a set from the considered classes, the eigenvalues of the quotient matrix are the maximum and the minimum eigenvalues of the graph. For D(m, 0), we show the existence of a third, intermediate, class of completely regular sets with the same property. [ABSTRACT FROM AUTHOR]

We study the following combinatorial version of the Slepian–Wolf coding scheme. Two isolated Senders are given binary strings $X$ and $Y$ , respectively; the length of each string is equal to $n$ , and the Hamming distance between the strings is at most $\alpha n$. The Senders compress their strings and communicate the results to the Receiver. Then, the Receiver must reconstruct both the strings $X$ and $Y$. The aim is to minimize the lengths of the transmitted messages. For an asymmetric variant of this problem (where one of the Senders transmits the input string to the Receiver without compression) with deterministic encoding, a nontrivial bound was found by Orlitsky and Viswanathany. In this paper, we prove a new lower bound for the schemes with syndrome coding, where at least one of the Senders uses linear encoding of the input string. For the combinatorial Slepian–Wolf problem with randomized encoding, the theoretical optimum of communication complexity was known earlier, even though effective protocols with optimal lengths of messages remained unknown. We close this gap and present a polynomial-time-randomized protocol that achieves the optimal communication complexity. [ABSTRACT FROM AUTHOR]

New lower and upper bounds on the reliability function of typewriter channels are given. Our lower bounds improve upon the (multiletter) expurgated bound of Gallager, furnishing a new and simple counterexample to a conjecture made in 1967 by Shannon, Gallager and Berlekamp on its tightness. The only other known counter example is due to Katsman, Tsfasman and Vlăduţ who used algebraic-geometric codes on a $q$ -ary symmetric channels, $q\geq 49$. Here we prove, by introducing dependence between codewords of a random ensemble, that the conjecture is false even for a typewriter channel with $q=4$ inputs. In the process, we also demonstrate that Lovász’s proof of the capacity of the pentagon was implicitly contained (but unnoticed!) in the works of Jelinek and Gallager on the expurgated bound done at least ten years before Lovász. In the opposite direction, new upper bounds on the reliability function are derived for channels with an odd number of inputs by using an adaptation of Delsarte’s linear programming bound. First, we derive a bound based on the minimum distance, which combines Lovász’s construction for bounding the graph capacity with the McEliece-Rodemich-Rumsey-Welch construction for bounding the minimum distance of codes in the Hamming space. Then, for the particular case of cross-over probability 1/2, we derive an improved bound by also using the method of Kalai and Linial to study the spectrum distribution of codes. [ABSTRACT FROM AUTHOR]

We prove that any variant of the GPT cryptosystem which uses a right column scrambler over the extension field as advocated by the works of Gabidulin et al. with the goal to resist to Overbeck’s structural attack are actually still vulnerable to that attack. We show that by applying the Frobenius operator appropriately on the public key, it is possible to build a Gabidulin code having the same dimension as the original secret Gabidulin code but with a lower length. In particular, the code obtained by this way corrects less errors than the secret one but its error correction capabilities are beyond the number of errors added by a sender. Consequently, an attacker is able to decrypt any ciphertext with this degraded Gabidulin code. We also considered the case where an isometric transformation is applied in conjunction with a right column scrambler which has its entries in the extension field. We proved that this protection is useless both in terms of performance and security. Consequently, our results show that all the existing techniques aiming to hide the inherent algebraic structure of Gabidulin codes have failed. [ABSTRACT FROM AUTHOR]