Search

This study designs a training system for hand rehabilitation on the basis of augmented reality technology, which enables patients to simultaneously interact with real and virtual environments. The system framework is introduced, and four rehabilitation programs, namely, trajectory training, shelf training, batting training, and spile training, are presented. As a requirement of hand rehabilitation training, a color marker that is suitable for hand rehabilitation training is adopted. Following the Hamming coding principle, this marker is designed as a 7 × 7 square that is filled up by four designated colors with a binary bit of '0' or '1'. The check code in each row of the color marker is applied to restore the occluded binary bits, solve the occlusion issue of color markers, and complete the tracking registration of the color markers. The effectiveness of the developed system is evaluated via a usability study and questionnaires. The evaluation provides positive results. Therefore, the developed system has potential as an effective rehabilitation system for upper limb impairment. [ABSTRACT FROM AUTHOR]

Hashing methods aim to learn a set of hash functions which map the original features to compact binary codes with similarity preserving in the Hamming space. Hashing has proven a valuable tool for large-scale information retrieval. We propose a column generation based binary code learning framework for data-dependent hash function learning. Given a set of triplets that encode the pairwise similarity comparison information, our column generation based method learns hash functions that preserve the relative comparison relations within the large-margin learning framework. Our method iteratively learns the best hash functions during the column generation procedure. Existing hashing methods optimize over simple objectives such as the reconstruction error or graph Laplacian related loss functions, instead of the performance evaluation criteria of interest-multivariate performance measures such as the AUC and NDCG. Our column generation based method can be further generalized from the triplet loss to a general structured learning based framework that allows one to directly optimize multivariate performance measures. For optimizing general ranking measures, the resulting optimization problem can involve exponentially or infinitely many variables and constraints, which is more challenging than standard structured output learning. We use a combination of column generation and cutting-plane techniques to solve the optimization problem. To speed-up the training we further explore stage-wise training and propose to optimize a simplified NDCG loss for efficient inference. We demonstrate the generality of our method by applying it to ranking prediction and image retrieval, and show that it outperforms several state-of-the-art hashing methods. [ABSTRACT FROM AUTHOR]

Content-addressable memories (CAMs) are a type of memory that receives an input search key and compares it to every entry of a table of stored keys. If there is a match, they return the corresponding address where the value was found. Alternatively, they can include a related Random Access Memory (RAM) that is accessed with the matching address, returning the corresponding data values. To protect a CAM with associated RAM against errors, parity or error-correction codes (ECCs) are typically used. They usually protect the CAM and the RAM information separately incurring in additional storage needs. This paper proposes a scheme to protect some configurations of CAM with its associated RAM from errors with a single ECC code. This ECC code can be used to provide advanced error correction to the combination of the key and data values stored in the CAM and the RAM, but it can also be applied in a modular way to provide simpler protection to the key or to the values individually. [ABSTRACT FROM AUTHOR]

The Hamming code is a well-known error correction code and can correct a single error in an input vector of size n bits by adding log n parity checks. A new parallel implementation of the code is presented, using a hierarchical structure of n processors in log n layers. All the processors perform similar simple tasks, and need only a few bytes of internal memory. [ABSTRACT FROM AUTHOR]

The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the generalized Hamming weights of three classes of linear codes constructed through defining sets and determine them partly for some cases. Particularly, in the semiprimitive case we solve a problem left in Yang et al. (2015) [30] . [ABSTRACT FROM AUTHOR]

This research addresses the problem of finding a minimum Hamming Weight by proposing a left-to-right recoding of integers (from the most significant bit to the less significant one). This representation is the enhanced and modified version of a well-known recoding method called Generalized Non-Adjacent Form (G-NAF). Scanning the digits from the left-to-right is called Modified Generalized Signed Digit Non-Adjacent Form (MGSDNAF), which unlike the GNAF, presents the 'nice property' to be obtained. A 'nice property' is one that is based on intuition and is particularly desirable to be obtained in a given context. This processing direction is of great importance because a table of pre-computed values may be used to speed up the scalar multiplication only for that direction. A subsequent advantage is that recoding the exponent in advance is not required. This results in better performances in both running time and memory space. This representation method can reduce the Hamming Weight of integers from about 21.6% for radix 3 to 15.1% for radix 9. These numbers for G-NAF recoding are 16.7% and 8.9% respectively. Comparing these numbers together shows that efficiency of the proposed method in reducing the Hamming Weight is more than the efficiency of G-NAF, which is from 30% (for radix 3) to more than 65% (for radix 9) more efficient in reducing the Hamming Weight. Finally, two radix 3 single scalar multiplication methods for Elliptic Curve Cryptography (ECC), which are based on G-NAF and Left-to-Right MGSDNAF, are compared in order to examine the application of the proposed method in cryptography. The results show that the proposed method can reduce the number of underlying arithmetic operations in single scalar multiplication by 14.1% while G-NAF can only reduce this number by 11.5%. [ABSTRACT FROM AUTHOR]

In this work we present a correspondence between the steganographic systems and error correcting codes. We propose a new steganographic protocol based on 3-error-correcting primitive BCH codes. We show that this new protocol has much better parameters than protocols which we get from Hamming codes or from the 2-error-correcting primitive BCH codes, for high levels of incorporation. [ABSTRACT FROM AUTHOR]

A number of state-of-the-art image retrieval systems have been built upon non-aggregated techniques such as Hamming Embedding (HE) and Selective Match Kernel (SMK). However, the retrieval performances of these techniques are directly affected by the quality of feature matching during the search process. In general, undesirable matched results appear mainly due to the following three aspects: (1) the locality of local features, (2) the quantization errors and (3) the phenomenon of burstiness. In this paper, starting from the framework of SMK, an in-depth study of the integration of Twin Feature (TF) and Similarity Maximal Matching (SMM) is fully investigated. To be specific, two effective modifications based on TF and SMM are proposed to further improve the quality of feature matching. On one hand, the original float vectors of TF are replaced with efficient binary signatures, which achieve relatively high efficiency and comparable accuracy of retrieval. On the other hand, Dynamic Normalization (DN) is designed to effectively control the impact of penalization generated by SMM and improve the performance with almost no extra cost. At last, an efficient image retrieval system is designed and realized based on a cloud-based heterogeneous computing framework through Apache Spark and multiple GPUs to deal with large-scale tasks. Experimental results demonstrate that the proposed system can greatly refine the visual matching process and improve image retrieval results. [ABSTRACT FROM AUTHOR]

This paper studies codes that correct a burst of deletions or insertions. Namely, a code will be called a $b$ -burst-deletion/insertion-correcting code if it can correct a burst of deletions/insertions of any $b$ consecutive bits. While the lower bound on the redundancy of such codes was shown by Levenshtein to be asymptotically $\log (n)+b-1$ , the redundancy of the best code construction by Cheng et al. is $b(\log (n/b+1))$ . In this paper, we close on this gap and provide codes with redundancy at most $\log (n) + (b-1)\log (\log (n)) +b -\log (b)$ . We first show that the models of insertions and deletions are equivalent and thus it is enough to study codes correcting a burst of deletions. We then derive a non-asymptotic upper bound on the size of $b$ -burst-deletion-correcting codes and extend the burst deletion model to two more cases: 1) a deletion burst of at most $b$ consecutive bits and 2) a deletion burst of size at most $b$ (not necessarily consecutive). We extend our code construction for the first case and study the second case for $b=3,4$ . [ABSTRACT FROM PUBLISHER]

We define generalized Hamming weights for almost affine codes. We show that this definition is natural, since we can extend some well-known properties of the generalized Hamming weights for linear codes, to almost affine codes. In addition, we discuss the duality of almost affine codes, and of the smaller class of multilinear codes. [ABSTRACT FROM PUBLISHER]

The study of frequency-hopping sequences (FHSs) has been focused on the establishment of theoretical bounds for the parameters of FHSs as well as on the construction of optimal FHSs with respect to the bounds. Peng and Fan (IEEE Trans Inf Theory 50(9):2149-2154, 2004) derived two lower bounds on the maximum nontrivial Hamming correlation of an FHS set, which is an important indicator in measuring the performance of an FHS set employed in practice. In this paper, we obtain two main results. We study the construction of new optimal frequency-hopping sequence sets by using cyclic codes over finite fields. Let $$\mathcal {C}$$ be a cyclic code of length n over a finite field $$\mathbb {F}_q$$ such that $$\mathcal {C}$$ contains the one-dimensional subcode $$ \mathcal {C}_0=\{(\alpha ,\alpha ,\ldots ,\alpha )\in \mathbb {F}_q^n\,|\,\alpha \in \mathbb {F}_q\}. $$ Two codewords of $$\mathcal {C}$$ are said to be equivalent if one can be obtained from the other through applying the cyclic shift a certain number of times. We present a necessary and sufficient condition under which the equivalence class of any codeword in $$\mathcal {C}\setminus \mathcal {C}_0$$ has size n. This result addresses an open question raised by Ding et al. (IEEE Trans Inf Theory 55(7):3297-3304, 2009). As a consequence, three new classes of optimal FHS sets with respect to the Singleton bound are obtained, some of which are also optimal with respect to the Peng-Fan bound at the same time. We also show that the two Peng-Fan bounds are, in fact, identical. [ABSTRACT FROM AUTHOR]

This paper describes a full-entropy 128-b key generation platform based on a 1024-b hybrid physically unclonable function (PUF) array, fabricated in 14-nm trigate high-k/metal-gate CMOS. Delay-hardened hybrid PUF cells use differential clock delay insertion to favor circuit evaluation in the desired direction while leveraging burn-in-induced aging for selective bit destabilization enabling quick identification and masking of unstable cells, and subsequent temporal-majority-voting with soft dark-bit masking to reduce PUF bit error by 3.9 times to 1.45% resulting in ~5 ppb failure probability. A stable full-entropy 128-b key is finally generated from the 1024 raw PUF bits using BCH error correction and AES-CBC-based entropy extraction. An all-digital design with compact PUF cell layout occupying 1.84~\mu \textm^2 achieves: 1) 4-fJ/b energy-efficiency with 3-μW leakage at 0.65 V, 70 °C; 2) peak operating frequency of 1 GHz resulting in 1.2-μs key generation latency; 3) robust operation with stable key generation across 0.55–0.75 V, and 25 °C–110 °C; 4) 14 times separation between intra/inter-PUF hamming distances with 0.99993 entropy ensuring cryptographic quality randomness and uniqueness; 5) 48% higher PUF stability with long-term aging by leveraging transistor degradation to reinforce favorable cell bias; and 6) resiliency to power cycling attacks with common centroid clock routing measured from 49.5% hamming distance between array’s evaluation and wake-up states. [ABSTRACT FROM AUTHOR]

A set X in the Euclidean space R d is an m -distance set if the set of Euclidean distances between two distinct points in X has size m . An m -distance set X in R d is maximal if there does not exist a vector x in R d such that the union of X and { x } still has only m distances. Bannai et al. (2012) investigated maximal m -distance sets that contain the Euclidean representation of the Johnson graph J ( n , m ) . In this paper, we consider the same problem for the Hamming graph H ( n , m ) . The Euclidean representation of H ( n , m ) is an m -distance set in R m ( n − 1 ) . We prove that if the representation of H ( n , m ) is not maximal as an m -distance set for some m , then the maximum value of n is m 2 + m − 1 . Moreover we classify the largest m -distance sets that contain the representation of H ( n , m ) for n ≥ 2 and m ≤ 4 . We also classify the maximal 2 -distance sets that are in R 2 n − 1 and contain the representation of H ( n , 2 ) for n ≥ 2 . [ABSTRACT FROM AUTHOR]

Molecular Communications is a promising area with significant potential applications. To enhance the reliability of the transmission process, self-orthogonal convolutional codes (SOCCs) are proposed and investigated with respect to both bit error rate (BER) and energy efficiency. The codes are compared to both an un-coded system and one that employs Hamming codes to show that they can provide a benefit for molecular communication systems. The influence of the channel memory is also analysed in this paper. In addition, taking into account the extra energy required to implement the coding, the critical distance is investigated as another performance metric for nano-to-nano device communication, nano-to-macro device communication and macro-to-nano device communication. Considering the transmission distance and the operating BER of the designed system, the designer can determine whether the use of coding is beneficial or which code better suits the system. [ABSTRACT FROM AUTHOR]

There is a limited class of perfect codes with respect to the classical Hamming metric. There are other kind of metrics with respect to which perfect codes have been investigated viz. poset metric, block metric and poset block metric. Given the minimal elements of a poset, a necessary and sufficient condition for -perfectness of a poset block code has been derived. A necessary and sufficient condition for a poset block code to be -perfect has also been considered. Further, for each , , a sufficient condition that ensures the existence of a poset block structure which turns a given code into an -perfect poset block code has been obtained. Several illustrations of well known codes to be -perfect for specific values of have been explored. [ABSTRACT FROM AUTHOR]

Cyclic subspace codes gained a lot of attention especially because they may be used in random network coding for correction of errors and erasures. Roth, Raviv and Tamo in 2018 established a connection between cyclic subspace codes (with certain parameters) and Sidon spaces. These latter objects were introduced by Bachoc, Serra and Zémor in 2017 in relation with the linear analogue of Vosper's Theorem. This connection allowed Roth, Raviv and Tamo to construct large classes of cyclic subspace codes with one or more orbits. In this paper we will investigate cyclic subspace codes associated to a set of Sidon spaces, that is cyclic subspace codes with more than one orbit. Moreover, we will also use the geometry of linear sets to provide some bounds on the parameters of a cyclic subspace code. Conversely, cyclic subspace codes are used to construct families of linear sets which extend a class of linear sets recently introduced by Napolitano, Santonastaso, Polverino and the author. This yields large classes of linear sets with a special pattern of intersection with the hyperplanes, defining rank metric and Hamming metric codes with only three distinct weights. [ABSTRACT FROM AUTHOR]

The Rosenbloom–Tsfasman metric has attracted the attention of many researchers as a generalization of the Hamming metric that is relevant to practical problems. Codes for this metric were considered. In particular, Reed–Solomon codes were generalized to be compatible with this metric. In this paper, a generalization of BCH codes for the Rosenbloom–Tsfasman metric is proposed. This generalization is based on considering BCH codes as subfield subcodes of Reed–Solomon codes. By characterizing these subfield subcodes, an explicit construction of BCH codes for the Rosenbloom–Tsfasman metric is provided. Two important properties of Reed–Solomon codes and BCH codes for the Rosenbloom–Tsfasman metric are studied and compared with those for the Hamming metric. These properties are cyclic structure and duality. The approach is based on Galois-Fourier transforms associated with Hasse derivatives. [ABSTRACT FROM PUBLISHER]

We give a randomized reduction for the Rank Syndrome Decoding problem and Rank Minimum Distance problem for rank codes over extension fields. Our results are based on embedding linear codes in the Hamming space into linear codes over an extension field equipped with the rank metric. We prove that if any of the previous problems for the rank metric is in ZPP = RP $\cap $ coRP, then we would have NP = ZPP. We also give complexity results for the respective rank metric approximation problems. [ABSTRACT FROM PUBLISHER]

Most data hiding schemes change the least significant bits to conceal messages in the cover images. Matrix encoding scheme is a well known scheme in this field. The matrix encoding proposed by Crandall can be used in steganographic data hiding methods. Hamming codes are kinds of cover codes. 'Hamming + 1' proposed by Zhang et al. is an improved version of matrix encoding steganography. The embedding efficiency of 'Hamming + 1' is very high for data hiding, but the embedding rate is low. Our proposed 'Hamming + 3' scheme has a slightly reduced embedding efficiency, but improve the embedding rate and image quality. 'Hamming + 3' is applied to overlapped blocks, which are composed of 2+3 pixels, where k=3. We therefore propose verifying the embedding rate during the embedding and extracting phases. Experimental results show that the reconstructed secret messages are the same as the original secret message, and the proposed scheme exhibits a good embedding rate compared to those of previous schemes. [ABSTRACT FROM AUTHOR]

All test patterns are decoded in the conventional Chase‐2 algorithm, but only a few candidate codewords are derived. In this work, a highly efficient Chase‐2 decoding algorithm has been proposed, where only the test patterns that can be decoded into distinct candidate codewords are processed. It means that the total number of decoding attempts is reduced from that of the test patterns to that of the candidate codewords, which consequently reduces the complexity, especially in high signal‐to‐noise ratio (SNR) region. The criterion of the test pattern selection is based on the property of minimum Hamming distance, it can be expected that the proposed algorithm can be applied to all linear block codes without performance degradation compared to the conventional Chase‐2 algorithm. [ABSTRACT FROM AUTHOR]

We provide a geometric characterization of k -dimensional F q m -linear sum-rank metric codes as tuples of F q -subspaces of F q m k. We then use this characterization to study one-weight codes in the sum-rank metric. This leads us to extend the family of linearized Reed-Solomon codes in order to obtain a doubly-extended version of them. We prove that these codes are still maximum sum-rank distance (MSRD) codes and, when k = 2 , they are one-weight, as in the Hamming-metric case. We then focus on constant rank-profile codes in the sum-rank metric, which are a special family of one weight-codes, and derive constraints on their parameters with the aid of an associated Hamming-metric code. Furthermore, we introduce the n -simplex codes in the sum-rank metric, which are obtained as the orbit of a Singer subgroup of GL (k , q m). They turn out to be constant rank-profile – and hence one-weight – and generalize the simplex codes in both the Hamming and the rank metric. Finally, we focus on 2-dimensional one-weight codes, deriving constraints on the parameters of those which are also MSRD, and we find a new construction of one-weight MSRD codes when q = 2. [ABSTRACT FROM AUTHOR]

A code C in the Hamming metric, that is, is a subset of the vertex set V Γ of the Hamming graph Γ = H (m , q) , gives rise to a natural distance partition { C , C 1 , ... , C ρ } , where ρ is the covering radius of C. Such a code C is called completely transitive if the automorphism group Aut (C) acts transitively on each of the sets C , C 1 , ..., C ρ. A code C is called 2-neighbour-transitive if ρ ⩾ 2 and Aut (C) acts transitively on each of C , C 1 and C 2. Let C be a completely transitive code in a binary (q = 2) Hamming graph having full automorphism group Aut (C) and minimum distance δ ⩾ 5. Then it is known that Aut (C) induces a 2-homogeneous action on the coordinates of the vertices of the Hamming graph. The main result of this paper classifies those C for which this induced 2-homogeneous action is not an affine, linear or symplectic group. We find that there are 13 such codes, 4 of which are non-linear codes. Though most of the codes are well-known, we obtain several new results. First, a non-linear completely transitive code that does not explicitly appear in the existing literature is constructed, as well as a related non-linear code that is 2-neighbour-transitive but not completely transitive. Moreover, new proofs of the complete transitivity of several codes are given. Additionally, we consider the question of the existence of distance-regular graphs related to the completely transitive codes appearing in our main result. [ABSTRACT FROM AUTHOR]

We consider the problem of the discrete-message transmission using the codes on the basis of the Shannon theorem, the Feinstein lemma, and the Hamming codes. In this case, the transmission quality is estimated using deterministic rather than random couplings among the messages and signals. It is shown that the coding redundancy, as well as the error-free transmission condition are not sufficient for realizing such a transmission. The signal-to-noise ratio is a more accurate parameter determining the transmission quality. The use of the Hamming code for long message sequences becomes efficient only if the threshold value of the signal-to-noise ratio is exceeded. [ABSTRACT FROM AUTHOR]

Distributed arithmetic coding (DAC) is a variant of AC that can realize Slepian-Wolf coding in a nonlinear way. In our previous work, we defined codebook cardinality spectrum (CCS) and Hamming distance spectrum (HDS) for DAC. In this paper, we make use of CCS and HDS to analyze tailed DAC, which is a form of DAC that, as traditional AC, maps the last few symbols of each source block onto non-overlapped intervals. First, we derive the exact HDS formula for tailless DAC, a form of DAC that maps all the symbols of each source block onto overlapped intervals, and show that the HDS formula previously given is in fact approximation. Then, the HDS formula is extended to tailed DAC. Using CCS, we also deduce the average codebook cardinality, which is closely related to decoding complexity, and rate loss of tailed DAC. The effects of tail length are extensively analyzed. It is revealed that by increasing tail length to a value not close to the bitstream length, closely spaced codewords within the same codebook can be removed at the cost of a higher decoding complexity and a larger rate loss. Finally, theoretical analyses are verified by experiments. [ABSTRACT FROM PUBLISHER]

Due to the significant growth of video data over the Internet, video steganography has become a popular choice. The effectiveness of any steganographic algorithm depends on the embedding efficiency, embedding payload, and robustness against attackers. The lack of the preprocessing stage, less security, and low quality of stego videos are the major issues of many existing steganographic methods. The preprocessing stage includes the procedure of manipulating both secret data and cover videos prior to the embedding stage. In this paper, we address these problems by proposing a novel video steganographic method based on Kanade-Lucas-Tomasi (KLT) tracking using Hamming codes (15, 11). The proposed method consists of four main stages: a) the secret message is preprocessed using Hamming codes (15, 11), producing an encoded message, b) face detection and tracking are performed on the cover videos, determining the region of interest (ROI), defined as facial regions, c) the encoded secret message is embedded using an adaptive LSB substitution method in the ROIs of video frames. In each facial pixel 1 LSB, 2 LSBs, 3 LSBs, and 4 LSBs are utilized to embed 3, 6, 9, and 12 bits of the secret message, respectively, and d) the process of extracting the secret message from the RGB color components of the facial regions of stego video is executed. Experimental results demonstrate that the proposed method achieves higher embedding capacity as well as better visual quality of stego videos. Furthermore, the two preprocessing steps increase the security and robustness of the proposed algorithm as compared to state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. Strictly optimal FHSs are those FHSs with optimal partial Hamming autocorrelation irrespective of the correlation window length. In this paper, strictly optimal FHSs are investigated from a combinatorial approach. A generic connection between strictly optimal FHSs and disjoint cyclic perfect Mendelsohn difference families is established. By virtue of this connection, new strictly optimal FHSs are generated from some disjoint CPMDFs. These strictly optimal FHSs have new parameters not covered in the literature. [ABSTRACT FROM AUTHOR]

In the secure cooperative source-coding problem that we consider, Encoder 1 and Decoder 1 observe, respectively, a pair of independent identically distributed (i.i.d.) correlated sources and wish to communicate the first source to Decoder 2 subject to a distortion constraint. Encoder 1 sends a message to both the decoders over a public nonsecure channel, and then Decoder 1—the helper—sends a message just to Decoder 2 over a secure channel. An eavesdropper, which has access to memoryless side-information that is correlated with the first source, intercepts the message sent by Encoder 1 and based on both wishes to minimize its uncertainty about the first source. The secrecy measure of the system is the equivocation of the first source at the eavesdropper. We determine the rates equivocation region for this problem assuming that conditioned on the side-information of Decoder 1 the eavesdropper’s side-information is independent of the first source. To that end, we derive an inner and an outer bound that depend explicitly on the proportional rate that Encoder 1 spends in the cooperation process. Subsequently, we evaluate this region for the case of a doubly symmetric binary source and Hamming distortion. [ABSTRACT FROM PUBLISHER]

A code is said to be propelinear if its automorphism group contains a subgroup which acts on the codewords regularly. Such a subgroup is called a propelinear structure on the code. With the aid of computer, we enumerate all propelinear structures on the Nordstrom-Robinson code and analyze the problem of extending them to propelinear structures on the extended Hamming code of length 16. The latter result is based on the description of partitions of the Hamming code of length 16 into Nordstrom-Robinson codes via Fano planes, presented in the paper. As a result, we obtain a record-breaking number of propelinear structures in the class of extended perfect codes of length 16. [ABSTRACT FROM AUTHOR]

Linear partition Arihant (LPA) codes have already been introduced by the author in [3]. Also, the concept of P-bursts in block coding has been formulated by the author in [4]. In this paper, we obtain a necessary bound which is infact an extension of Hamming sphere upper bound over the number of parity checks required in an LPA code to correct a message which has both clustered block errors (or P-burst errors) as well as occasional/random block errors with wright constraint. We also obtain bounds for LPA codes correcting block errors with bounded intensity. [ABSTRACT FROM AUTHOR]

The way of combination of Product Perfect Codes (PPCs) is based on the theory of short codes constructing long codes. PPCs have larger embedding rate than Hamming codes by expending embedding columns in a coding block, and they have been proven to enhance the performance of the steganographic F5 method. In this paper, the proposed modified product codes called MPCs are introduced as an efficient way to embed more data than PPCs by increasing 2r2-1-r2 embedding columns. Unlike PPC, the generation of the check matrix H in MPC is random, and it is different from PPC. In addition a simple solving way of the linear algebraic equations is applied to figure out the problem of expending embedding columns or compensating cases. Furthermore, the MPCs over Z4 have been proposed to further enhance not only the performance but also the computation speed which reaches O(n1 + s). Finally, the proposed Z4-MPC intends to maximize the embedding rate with maintaining less distortion, and the performance surpasses the existing improved product perfect codes. The performance of large embedding rate should have the significance in the high-capacity of covert communication. [ABSTRACT FROM AUTHOR]

The units of the chain ring R a = F p m [ u ] 〈 u a 〉 = F p m + u F p m + ⋯ + u a − 1 F p m are partitioned into a distinct types. It is shown that for any unit Λ of Type k , a unit λ of Type k ∗ can be constructed, such that the class of λ -constacyclic of length p s of Type k ∗ codes is one-to-one correspondent to the class of Λ -constacyclic codes of the same length of Type k via a ring isomorphism. The units of R a of the form Λ = Λ 0 + u Λ 1 + ⋯ + u a − 1 Λ a − 1 , where Λ 0 , Λ 1 , … , Λ a − 1 ∈ F p m , Λ 0 ≠ 0 , Λ 1 ≠ 0 , are considered in detail. The structure, duals, Hamming and homogeneous distances of Λ -constacyclic codes of length p s over R a are established. It is shown that self-dual Λ -constacyclic codes of length p s over R a exist if and only if a is even, and in such case, it is unique. Among other results, we discuss some conditions when a code is both α - and β -constacyclic over R a for different units α , β . [ABSTRACT FROM AUTHOR]

The column Hamming distance of a convolutional code determines the error correction capability when streaming over a class of packet erasure channels. We introduce a metric known as the column sum rank that parallels the column Hamming distance when streaming over a network with link failures. We prove the rank analogues of several known column Hamming distance properties and introduce a new family of convolutional codes that maximize the column sum rank up to the code memory. Our construction involves finding a class of super-regular matrices that preserve this property after multiplication with non-singular block diagonal matrices in the ground field. [ABSTRACT FROM AUTHOR]

Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHSs and FHS sets with optimal partial Hamming correlation. We first establish a correspondence between FHS sets with optimal partial Hamming correlation and multiple partition-type balanced nested cyclic difference packings with a special property. By virtue of this correspondence, some FHSs and FHS sets with optimal partial Hamming correlation are constructed from various combinatorial structures, such as cyclic difference packings and cyclic relative difference families. As a consequence, our constructions yield new FHSs and FHS sets with optimal partial Hamming correlation. [ABSTRACT FROM AUTHOR]

We investigate the second order asymptotics (source dispersion) of the successive refinement problem. Similar to the classical definition of a successively refinable source, we say that a source is strongly successively refinable if successive refinement coding can achieve the second order optimum rate (including the dispersion terms) at both decoders. We establish a sufficient condition for strong successive refinability. We show that any discrete source under Hamming distortion and the Gaussian source under quadratic distortion are strongly successively refinable. We also demonstrate how successive refinement ideas can be used in point-to-point lossy compression problems in order to reduce complexity. We give two examples, the binary-Hamming and Gaussian-quadratic cases, in which a layered code construction results in a low complexity scheme that attains optimal performance. For example, when the number of layers grows with the block length $n$ , we show how to design an O(n^{\log (n)}) algorithm that asymptotically achieves the rate-distortion bound. [ABSTRACT FROM AUTHOR]

In this paper we find some bounds for the relative generalized Hamming weights of some codes parameterized by a set of monomials of the same degree. Also we compare the relative generalized Hamming weights of the codes CX(d) and CX'(d) when X' is embedded in X. We use these results to obtain some lower bounds for the relative generalized Hamming weights of the codes parameterized by the edges of any connected bipartite graph with bipartition (V1, V2) and where |V1| = n1, |V2| = n2, in terms of the relative generalized Hamming weights of the codes associated to the projective tori ... and .... [ABSTRACT FROM AUTHOR]

Relative two-weight codes have been studied due to their applications to wiretap channel and secret sharing. It has been shown that these codes form a large family, which includes dual Hamming codes and subcodes of punctured Reed-Muller codes as special instances. This work studies the properties of relative two-weight codes with regard to efficient decoding. More specifically, the trellis complexity, which determines the complexity of Viterbi algorithm based decoding and pseudoredundancy that measures the performance and complexity of linear programming decoding are studied for relative two-weight codes. Separating properties of these codes have been identified and proved first. Based on the results of separating properties, the trellis complexity of binary relative two-weight codes is fully determined. An upper bound on the pseudoredundancy of binary relative two-weight codes is derived. [ABSTRACT FROM AUTHOR]

Constructions of quantum caps in projective space PG( r, 4) by recursive methods and computer search are discussed. For each even n satisfying $$n\ge 282$$ and each odd z satisfying $$z\ge 275$$ , a quantum n-cap and a quantum z-cap in $$PG(k-1, 4)$$ with suitable k are constructed, and $$[[n,n-2k,4]]$$ and $$[[z,z-2k,4]]$$ quantum codes are derived from the constructed quantum n-cap and z-cap, respectively. For $$n\ge 282$$ and $$n\ne 286$$ , 756 and 5040, or $$z\ge 275$$ , the results on the sizes of quantum caps and quantum codes are new, and all the obtained quantum codes are optimal codes according to the quantum Hamming bound. While constructing quantum caps, we also obtain many large caps in PG( r, 4) for $$r\ge 11$$ . These results concerning large caps provide improved lower bounds on the maximal sizes of caps in PG( r, 4) for $$r\ge 11$$ . [ABSTRACT FROM AUTHOR]

This paper considers a family of metrics to compare images based on their local descriptors. It encompasses the vector or locally aggregated descriptors descriptor and matching techniques such as hamming embedding. Making the bridge between these approaches leads us to propose a match kernel that takes the best of existing techniques by combining an aggregation procedure with a selective match kernel. The representation underpinning this kernel is approximated, providing a large scale image search both precise and scalable, as shown by our experiments on several benchmarks. We show that the same aggregation procedure, originally applied per image, can effectively operate on groups of similar features found across multiple images. This method implicitly performs feature set augmentation, while enjoying savings in memory requirements at the same time. Finally, the proposed method is shown effective for place recognition, outperforming state of the art methods on a large scale landmark recognition benchmark. [ABSTRACT FROM AUTHOR]

Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties are desirable in many synchronization and multiple-access systems. An FHS set is said to be strictly optimal if it has optimal partial Hamming correlation for any correlation window. In this paper, we derive upper bounds on the family sizes of FHS sets with respect to partial Hamming correlation from some classical bounds on error-correcting codes. We then present strictly optimal FHS sets having optimal family sizes with respect to one of the new bounds. In particular, our construction gives new parameters not covered in the literature. [ABSTRACT FROM AUTHOR]

Information retrieval in associative memories was studied in a recent paper by Yaakobi and Bruck (2012). Associations between memory entries give us the t -neighbourhood of an entry. In their model, an information unit is retrieved from the memory with the aid of input clues, which are chosen from a reference set. In this paper, we consider the situation where the information unit is found unambiguously using the associated t -neighbourhoods of the input clues. A varying number of input clues are allowed, but a limit mu on the maximum number of them is imposed. Of course, we would like mu to be as small as possible. We consider the problem over the binary Hamming space \mathbb F^n and focus on the minimum of mu , denoted by $\nu (n;t)$ . Using linear reference sets, we show that $\nu (n;2) \leq 5$ for any $n \geq 9$ . We also give infinite families of reference sets, which provide good bounds on $\nu (n;t)$ for $t=3$ . In addition, efficient methods are given to obtain bounds on $\nu (n;t)$ for any $t$ from known reference sets. We also discuss the applications of this model to the Levenshtein’s sequence reconstruction problem and the sensor network monitoring. [ABSTRACT FROM AUTHOR]

In this paper, we explore completely regular codes in the Hamming graphs and related graphs. Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression. In order to better understand these "arithmetic completely regular codes", we focus on cartesian products of completely regular codes and products of their corresponding coset graphs in the additive case. Employing earlier results, we are then able to prove a theorem which nearly classifies these codes in the case where the graph admits a completely regular partition into such codes (e.g, the cosets of some additive completely regular code). Connections to the theory of distance-regular graphs are explored and several open questions are posed. [ABSTRACT FROM AUTHOR]

In this Letter, a new error‐resilient router design for network‐on‐chips (NoCs) is proposed to effectively address various transient errors considering power efficiency and implementation complexity. To cope with the most probable error conditions, a selective error correction code (ECC) is embraced in router design, which combines an optimised double‐bit error‐correcting Bose–Chaudhuri–Hocquenghem (BCH) code and a single‐bit error‐correcting Hamming code. To reduce the inherent delay overhead of the BCH code, the parallel BCH coding scheme is designed and implemented into the proposed router. Furthermore, the associated ECC controller is designed for switching into an appropriate ECC mode without an additional delay at runtime. The proposed router is synthesised using 28 nm CMOS technology. Experimental results with a variety of common error conditions show that the proposed method improves the average latency by up to 13.8% and achieves up to 11.5% power reduction with the area increase of 5.7%, when compared to the conventional error correction scheme. [ABSTRACT FROM AUTHOR]

Error detection and correction codes provide reliable delivery of information signals. In general, these types of errors are generated in RAM chips [Error detection]. These errors can be detected and corrected by employing the error-detecting and error-correcting codes in RAMs. The most generalized scheme for detecting the error in error detecting technique is parity bit. In Single Error Correction- Triple Adjacent Error Detection (SECTAED) method, the parity bit can be extended to detect a single error as well as triple adjacent errors. Hence, SEC-TAED based hamming code is referred to as "Extended Hamming SEC-TAED codes." Hence, 82% of detection efficiency can be achieved in modified bit-reordered based SEC-TAED process. [ABSTRACT FROM AUTHOR]

• In consideration of privacy protection, we are the first to explore the universal attack against deep video hashing based on the UAH. • We also consider the data-free scenario and propose a method to perform the universal attack without access to the original videos. • We conduct extensive experiments to verify the effectiveness of our method under both white-box and black-box settings. While online video sharing becomes more popular, it also causes unconscious leakage of personal information in the video retrieval systems like deep hashing. A snoop can collect more users' private information from the video database by querying similar videos. This paper focuses on bypassing the deep video hashing based retrieval to prevent information from being maliciously collected. We propose universal adversarial head (UAH), which crafts adversarial query videos by prepending the original videos with a sequence of adversarial frames to perturb the normal hash codes in the Hamming space. This adversarial head can be generated only with a few natural videos, and mislead the retrieval system to return irrelevant videos when it is applied to most query videos. Furthermore, to obey the principle of information protection, we expand the proposed method to a data-free paradigm to generate the UAH, without access to users' original videos. Extensive experiments demonstrate the effectiveness of our method in misleading deep video hashing under both white-box and black-box settings. [ABSTRACT FROM AUTHOR]

This work investigates the structure of rank-metric codes in connection with concepts from finite geometry, most notably the q -analogues of projective systems and blocking sets. We also illustrate how to associate a classical Hamming-metric code to a rank-metric one, in such a way that various rank-metric properties naturally translate into the homonymous Hamming-metric notions under this correspondence. The most interesting applications of our results lie in the theory of minimal rank-metric codes, which we introduce and study from several angles. Our main contributions are bounds for the parameters of a minimal rank-metric codes, a general existence result based on a combinatorial argument, and an explicit code construction for some parameter sets that uses the notion of a scattered linear set. Throughout the paper we also show and comment on curious analogies/divergences between the theories of error-correcting codes in the rank and in the Hamming metric. [ABSTRACT FROM AUTHOR]