Related papers: Linear codes with few weights over $\mathbb{F}_{p}…

Let $p$ be a prime number. Irreducible cyclic codes of length $p^2-1$ and dimension $2$ over the integers modulo $p^h$ are shown to have exactly two nonzero Hamming weights. The construction uses the Galois ring of characteristic $p^h$ and…

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;\theta]-submodules of R_{k}[x;\theta]/\langle…

Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ and $R=\mathbb{F}_{p^m}[u]/\langle u^2\rangle=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ $(u^2=0)$, where $p$ is an odd prime and $m$ is a positive integer. For any $\alpha,\beta\in…

Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$, where $p$ is a prime, and $k, N$ be any positive integers. We denote $R_k=F_{p^m}[u]/\langle u^k\rangle =F_{p^m}+uF_{p^m}+\ldots+u^{k-1}F_{p^m}$ ($u^k=0$) and…

For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…

Let $p$ be an odd prime, and let $m$ be a positive integer satisfying $p^m \equiv 3~(\text{mod }4).$ Let $\mathbb{F}_{p^m}$ be the finite field with $p^m$ elements, and let $R=\mathbb{F}_{p^m}[u]/\left<u^2\right>$ be the finite commutative…

Following the approach by R. K\"otter and F. R. Kschischang, we study network codes as families of k-dimensional linear subspaces of a vector space F_q^n, q being a prime power and F_q the finite field with q elements. In particular,…

Let $q$ be a prime power. This paper provides a new class of linear codes that arises from the action of the alternating group on $\mathbb F_q[x_1,\dots,x_m]$ combined with the ideas in (M. Datta and T. Johnsen, 2022). Compared with…

There are exactly two non-commutative rings of size $4$, namely, $E = \langle a, b ~\vert ~ 2a = 2b = 0, a^2 = a, b^2 = b, ab= a, ba = b\rangle$ and its opposite ring $F$. These rings are non-unital. A subset $D$ of $E^m$ is defined with…

A generator matrix of a linear code $\C$ over $\gf(q)$ is also a matrix of the same rank $k$ over any extension field $\gf(q^\ell)$ and generates a linear code of the same length, same dimension and same minimum distance over $\gf(q^\ell)$,…

Let $\ell>0$ be a square-free integer congruent to 3 mod 4 and $\O_K$ the ring of integers of the imaginary quadratic field $K=Q(\sqrt{-\ell})$. Codes $C$ over rings $\O_K / p \O_K$ determine lattices $\Lambda_\ell (C) $ over $K$. If $ p…

The permutation groups of cyclic codes are widely applicable in determining the weight distribution of codes, decoding theory and various other areas. In this paper, by employing two distinct matrix representations, we can relate cyclic…

Let $R=\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ be a non-chain finite commutative ring, where $u^3=u$. In this paper, we mainly study the construction of quantum codes from cyclic codes over $R$. We obtained self-orthogonal codes over…

We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…

In this paper, a family of cyclic codes over $\mathbb{F}_{p}$ whose duals have five zeros is presented, where $p$ is an odd prime. Furthermore, the weight distributions of these cyclic codes are determined.

In the paper, we firstly study the algebraic structures of $\mathbb{Z}_p \mathbb{Z}_{p^k}$-additive cyclic codes and give the generator polynomials and the minimal spanning set of these codes. Secondly, a necessary and sufficient condition…

We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of…

The weight hierarchy of a linear code has been an important research topic in coding theory since Wei's original work in 1991. Choosing $ D=\Big\{(x,y)\in \Big(\F_{p^{s_1}}\times\F_{p^{s_2}}\Big)\Big\backslash\{(0,0)\}: f(x)+g(y)=0\Big\}$…

We define generalized Hamming weights for almost affine codes. We show how various aspects and applications of generalized Hamming weights for linear codes, such as Wei duality, generalized Kung's bound, profiles, connection to wire-tap…

We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…