We recall a classic lower bound on the minimum Hamming distance of constacyclic codes over finite fields, analogous to the well-known BCH bound for cyclic codes. This BCH-like bound serves as a foundation for proposing some minimum-distance lower bou...
We consider mixed Hamming packings, addressing the maximal cardinality of codes with a minimum codeword Hamming distance. We do not rely on any algebraic structure of the alphabets. We extend known-integer linear programming models of the problem to...
Given a linear code
Short or moderate-length non-binary low-density parity-check (NB-LDPC) codes have the potential applications in future low latency and high-reliability communication thanks to the strong error correction capability and parallel decoding. Because of t...
In this paper, we obtain upper bounds on the minimum distance for turbo codes using fourth degree permutation polynomial (4-PP) interleavers of a specific interleaver length and classical turbo codes of nominal 1/3 coding rate, with two recursive sys...
To enhance the reliability of UAV-to-Ground data transmission in SC-FDE, this study proposes a combined MMSE equalization and LDPC-RS concatenated code approach, utilizing source redundancy to mitigate errors in low-elevation G2A communication. The p...
Finger vein recognition has drawn increasing attention as one of the most popular and promising biometrics due to its high distinguishing ability, security, and non-invasive procedure. The main idea of traditional schemes is to directly extract featu...
The objective of this work is to analyze the importance of the product
Binary codes have a special place in coding theory since they are one of the most commonly used in practice. There are classes of codes specific only to the binary case. One such class is self-complementary codes. Self-complementary linear codes are...
In this paper, we generalize the construction of locally repairable codes (LRCs) by leveraging pairwise balanced designs (PBDs) and balanced incomplete block designs (BIBDs) to construct codes with nonuniform locality or nonuniform availability. Our...
Symbol-pair codes are a class of block codes with symbol-pair metrics designed to protect against pair errors that may occur in high-density data storage systems. Maximum distance separable (MDS) symbol-pair codes are optimal in the sense that they c...
The code distance is a critical parameter of quantum stabilizer codes (QSCs), and determining it—whether exactly or approximately—is known to be an NP-complete problem. However, its upper bound can be determined efficiently by some method...
The McEliece cryptosystem is a promising candidate for post-quantum public-key encryption. In this work, we propose q-ary codes over Gaussian integers for the McEliece system and a new channel model. With this one Mannheim error channel, errors are l...
The rapid development of machine learning, large language models, and related technologies has greatly increased the demand for data storage capacity. Therefore, the role of distributed storage systems in such applications has become more prominent....
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 ar...
The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem, together with the one-Mannh...
In this paper, new conditions on parameters in difference sets are derived to satisfy symplectic inner product, and new constructions of quantum stabilizer codes are proposed from the conditions. The conversion of the difference sets into parity-chec...
The Hasse derivative image of a repeated-root cyclic code is typically non-cyclic. This prevents a direct ideal-theoretic calculation of derivative-twisted intersections and first leads to cyclic containers and two-sided bounds. This paper shows that...
We study symplectic Galois-LCD codes over the finite non-chain ring
Square fiducial markers provide a robust and efficient way to establish visual references in camera localization tasks, combining reliable detection with unique identification through an embedded binary code. The robustness of these systems depends l...
This paper presents an approach to the construction of block error-correcting code for data transmission systems with short packets. The need for this is driven by the necessity of information interaction between objects of machine-type communication...
This paper considers three kinds of quasi-cyclic codes of index two with one generator or two generators and their applications in quantum code construction. In accordance with the algebraic structure of linear codes, we determine the lower bounds of...
We present a simple computational approach to assigning a measure of complexity and information/entropy to families of natural languages, based on syntactic parameters and the theory of error correcting codes. We associate to each language a binary s...
It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical...
In this paper, a new family of binary LRCs (BLRCs) with locality 2 and uneven availabilities for hot data is proposed, which has a high information symbol availability and low parity symbol availabilities for the local repair of distributed storage s...
Quantum error correcting codes (QECCs) play an important role in preventing quantum information decoherence. Good quantum stabilizer codes were constructed by classical error correcting codes. In this paper, Bose–Chaudhuri–Hocquenghem (BCH) codes ove...
The hull of a linear code, defined as its intersection with its dual code, plays an important role in the construction of entanglement-assisted quantum error-correcting codes. In particular, the hull dimension determines both the number of encoded qu...
In recent years, network coding has attracted widespread attention due to its important role in digital communication and network security. Among these, cyclic subspace codes have very important applications in error correction and rectification in r...
The distributed Goppa-coded generalized spatial modulation (DGC-GSM) scheme with the source, relay, and destination in cooperative communications is proposed, where the source and relay adopt different Goppa codes. Goppa codes have many advantages su...
Locally repairable codes (LRCs) are a new family of erasure codes used in distributed storage systems which have attracted a great deal of interest in recent years. For an
Solomonoff induction mixes all computable explanations with description-length weights, but it is incomputable. This theory-and-position paper argues that practical approximation must be category-native: one should first declare the mathematical cate...
This paper presents an experimental study where the mechanical behaviour of single-dowel timber connections made of acetylated Scots pine is compared with the behaviour of connections made from untreated Scots pine. The main aim was to evaluate the i...
The growing demand for extensive and reliable structural health monitoring resulted in the development of advanced optical sensing systems (OSS) that in conjunction with wireless optical networks (WON) are capable of extending the reach of optical se...
Non-circular or improper Gaussian signaling has proven beneficial in several interference-limited wireless networks. However, all implementable coding schemes are based on finite discrete constellations rather than Gaussian signals. In this paper, we...
In this paper, new construction methods of entanglement-assisted quantum error correction code (EAQECC) from circulant matrices are proposed. We first construct the matrices from two vectors of constraint size, and determine the isotropic subgroup. T...
Hydrogen gas storage place has been increasing daily because of its consumption. Hydrogen gas is a dream fuel of the future with many social, economic and environmental benefits to its credit. However, many hydrogen storage tanks exploded accidentall...
Due to the Software Defined Network (SDN) technology, Wireless Sensor Networks (WSNs) are getting wider application prospects for sensor nodes that can get new functions after updating program codes. The issue of disseminating program codes to every...
In this paper, a non-binary low-density parity-check (NB-LDPC) coded high-order continuous phase modulation (CPM) system is designed and optimized to improve power and iterative efficiencies. Firstly, the minimum squared normalized Euclidean distance...
We study cyclic codes over split two-branch finite local rings of the form
Let c be a proper k-coloring of a graph G. Let
This paper presents a new high-speed RGB image transmission system over Free-Space Optics (FSO) channel employing Optical Code Division Multiple Access (OCDMA) with Permutation Vector (PV) codes. Four RGB images are transmitted simultaneously at 10 G...
The widespread development in wireless technologies and the advancements in multimedia communication have brought about a positive impact on the performance of wireless transceivers. We investigate the performance of our three-stage turbo detected sy...
Symmetric cryptography is essential for secure communication as it ensures confidentiality by using shared secret keys. This paper proposes a novel substitution-permutation network (SPN) that integrates Latin squares, permutations, and Reed-Muller (R...
Orthogonal direct sum masking (ODSM) protects embedded cryptographic implementations against side-channel attacks by splitting the ambient space into a source code C carrying sensitive data and a complementary masking code D carrying fresh randomness...
Adder neural networks remove multiplication from convolution, yet their direct L1-distance datapath still requires subtraction, absolute-value generation, and wide accumulation. We address this cost by mapping the online L1 operation to minimum selec...
This paper proposes a resource optimized cascaded quantum surface repetition code architecture integrated with a Union Find (UF) enhanced hybrid decoder, which suppresses biased noise and improves the scalability of quantum error correction through s...
The time required for rescue is a critical factor for surviving a marine incident. The regulatory framework, International Maritime Organization (IMO) Polar Code, utilizes a risk-based approach. It states that the vessel operators are to define the t...
In the context of the high-speed development of 5G communications, high-performance decoding schemes for polar codes are a hot spot in channel coding research. Shift pruning successive cancellation list (SP-SCL) decoding aims to recover the correct p...
This paper presents a novel 160 Gbps free space optics (FSO) communication system for 6G applications. Polarization division multiplexing (PDM) is integrated with an optical code division multiple access (OCDMA) technique to form a PDM-OCDMA hybrid....
The advent of quantum computing threatens the long-term security of classical public-key cryptosystems: RSA and standard elliptic-curve cryptography are vulnerable to Shor’s algorithm, making quantum-resistant alternatives a priority for modern...
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