Related papers: Convolutional Codes of Goppa Type
This paper proposes a new family of recursive systematic convolutional codes, defined in the non-binary domain over different Galois fields GF(q) and intended to be used as component codes for the design of non-binary turbo codes. A general…
In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…
Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
Locally recoverable codes are widely used in distributed and cloud storage systems. The objective of this paper is to present a construction of near MDS codes with oval polynomials and then determine the locality of the codes. It turns out…
The construction of quantum error-correcting codes (QECCs) with good parameters is a hot topic in the area of quantum information and quantum computing. Quantum maximum distance separable (QMDS) codes are optimal because the minimum…
Cyclic codes and their various generalizations, such as quasi-twisted (QT) codes, have a special place in algebraic coding theory. Among other things, many of the best-known or optimal codes have been obtained from these classes. In this…
Large Language Models (LLMs) have demonstrated great promise in generating code, especially when used inside an evolutionary computation framework to iteratively optimize the generated algorithms. However, in some cases they fail to…
New families of maximum distance separable (MDS) codes are constructed from elliptic curves by exploiting their group structures. In contrast to classical constructions based on divisors supported at a single rational point, the proposed…
In this article we consider a new derivation mode for generalized communicating P systems (GCPS) corresponding to the functioning of population protocols (PP) and based on the sequential derivation mode and a fairness condition. We show…
Polarization-adjusted convolutional (PAC) codes were recently proposed and arouse the interest of the channel coding community because they were shown to approach theoretical bounds for the (128,64) code size. In this letter, we propose…
Maximum distance separable (in short, MDS), near MDS (in short, NMDS), and self-orthogonal codes play a pivotal role in algebraic coding theory, particularly in applications such as quantum communications and secret sharing scheme.…
A new design method for high rate, fully diverse ('spherical') space frequency codes for MIMO-OFDM systems is proposed, which works for arbitrary numbers of antennas and subcarriers. The construction exploits a differential geometric…
In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which…
Spatially coupled codes have been shown to universally achieve the capacity for a large class of channels. Many variants of such codes have been introduced to date. We discuss a further such variant that is particularly simple and is…
Generalized Product (GPC) Codes, an unification of Product Codes and Integrated Interleaved (II) Codes, are presented. Applications for approaches requiring local and global parities are described. The more general problem of extending…
Recently, Yaakobi et al. introduced codes for $b$-symbol read channels, where the read operation is performed as a consecutive sequence of $b>2$ symbols. In this paper, we establish a Singleton-type bound on $b$-symbol codes. Codes meeting…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
An ensemble of LDPC convolutional codes with parity-check matrices composed of permutation matrices is considered. The convergence of the iterative belief propagation based decoder for terminated convolutional codes in the ensemble is…
We introduce a new type of reduction of inversive difference polynomials that is associated with a partition of the basic set of automorphisms $\sigma$ and uses a generalization of the concept of effective order of a difference polynomial.…