相关论文: Galois LCD Codes over Finite Fields

This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are…

Greaves et al. (2022) extended frames over real or complex numbers to frames over finite fields. In this paper, we study the theory of frames over finite fields by incorporating the Galois inner products introduced by Fan and Zhang (2017),…

The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic…

It's well-known that maximum distance separable codes (in short, MDS) and linear complementary dual (in short, LCD) codes are very important in coding theory and practice. In 2023, Yue et al. [25] constructed three classes of LCD MDS codes…

Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required…

Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…

Linear complementary dual codes were defined by Massey in 1992, and were used to give an optimum linear coding solution for the two user binary adder channel. In this paper, we define the analog of LCD codes over fields in the ambient space…

In this work, we study and determine the dimensions of Euclidean and Hermitian hulls of two classical propagation rules, namely, the direct sum construction and the $(\mathbf{u},\mathbf{u+v})$-construction. Some new criteria for the…

Given $\texttt{S}|\texttt{R}$ a finite Galois extension of finite chain rings and $\mathcal{B}$ an $\texttt{S}$-linear code we define two Galois operators, the closure operator and the interior operator. We proof that a linear code is…

Linear complementary dual (LCD) codes introduced by Massey are the codes whose intersections with their dual codes are trivial. It can help to improve the security of the information processed by sensitive devices, especially against…

Due to some practical applications, linear complementary dual (LCD) codes and self-orthogonal codes have attracted wide attention in recent years. In this paper, we use simplicial complexes for construction of an infinite family of binary…

We consider two-dimensional $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_{q}$ of area $M N$, where $q$ is some power of prime $p$ with $\gcd(M,p)=1$ and $\gcd(N,p)=1$. With the help of common zero (CZ) set, we characterize…

We investigate two classes of extended codes and provide necessary and sufficient conditions for these codes to be non-GRS MDS codes. We also determine the parity check matrices for these codes. Using the connection of MDS codes with arcs…

The hulls of linear and cyclic codes have been extensively studied due to their wide applications. In this paper, the average dimension of the Hermitian hull of constacyclic codes of length $n$ over a finite field $\mathbb{F}_{q^2}$ is…

Let $\mathbb{F}_{q}$ denote the finite field of order $q,$ let $m_1,m_2,\cdots,m_{\ell}$ be positive integers satisfying $\gcd(m_i,q)=1$ for $1 \leq i \leq \ell,$ and let $n=m_1+m_2+\cdots+m_{\ell}.$ Let…

Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a…

A monomial-Cartesian code is an evaluation code defined by evaluating a set of monomials over a Cartesian product. It is a generalization of some families of codes in the literature, for instance toric codes, affine Cartesian codes and…

Let $q=p^m$ be a prime power and $e$ be an integer with $0\leq e\leq m-1$. $e$-Galois self-dual codes are generalizations of Euclidean $(e=0)$ and Hermitian ($e=\frac{m}{2}$ with even $m$) self-dual codes. In this paper, for a linear code…

MDS codes have diverse practical applications in communication systems, data storage, and quantum codes due to their algebraic properties and optimal error-correcting capability. In this paper, we focus on a class of linear codes and…

Given a parity-check matrix $H_m$ of a $q$-ary Hamming code, we consider a partition of the columns into two subsets. Then, we consider the two codes that have these submatrices as parity-check matrices. We say that anyone of these two…