Related papers: Linear codes with few weights over $\mathbb{F}_2+u…
We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry, and an application of Weil's theorem. We relate the weights appearing in the dual codes to the number of rational…
Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial…
In this work, we define a modification of a bordered construction for self-dual codes which utilises $\lambda$-circulant matrices. We provide the necessary conditions for the construction to produce self-dual codes over finite commutative…
Recently, linear codes with a few weights were widely investigated due to their applications in secret sharing schemes and authentication schemes. In this letter, we present a class of $q$-ary linear codes derived from irreducible cyclic…
Using theoretical results about the homogeneous weights for Frobenius rings, we describe the homogeneous weight for the ring family $R_k$, a recently introduced family of Frobenius rings which have been used extensively in coding theory. We…
In this paper, we give conditions for the existence of Hermitian self-dual $\Theta-$cyclic and $\Theta-$negacyclic codes over the finite chain ring $\mathbb{F}_q+u\mathbb{F}_q$. By defining a Gray map from $R=\mathbb{F}_q+u\mathbb{F}_q$ to…
We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a…
Coding theory and $t$-designs have close connections and interesting interplay. In this paper, we first introduce a class of ternary linear codes and study their parameters. We then focus on their three-weight subcodes with a special weight…
Let $\Bbb F_r$ be an extension of a finite field $\Bbb F_q$ with $r=q^m$. Let each $g_i$ be of order $n_i$ in $\Bbb F_r^*$ and $\gcd(n_i, n_j)=1$ for $1\leq i \neq j \leq u$. We define a cyclic code over $\Bbb F_q$ by $$\mathcal C_{(q, m,…
Cyclic codes over R have been introduced recently. In this paper, we study the cyclic codes over R and their $\Z_2$ image. Making use of algebraic structure, we find the some good $\Z_2$ codes of length 28.
Weight enumerators are important tools for deciphering the algebraic structure of the related code spaces and for understanding group actions on these spaces. Our study focuses on symmetrized weight enumerators of pairs of Type II codes…
We give results on the question of code optimality for linear codes over finite Frobenius rings for the homogeneous weight. This article improves on the existing Plotkin bound derived in an earlier paper, and suggests a version of a…
Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, some kinds of p-ary linear codes with few weights are constructed by use of the given de ning set,…
We present a family of reducible cyclic codes constructed as the direct sum of two different semiprimitive two-weight irreducible cyclic codes. This family generalizes the class of reducible cyclic codes that was reported in the main result…
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…
We study the structure of linear codes over the ring $B_k$ which is defined by $\mathbb{F}_{p^r}[v_1,v_2,\ldots,v_k]/\langle v_i^2=v_i,~v_iv_j=v_jv_i \rangle_{i,j=1}^k.$ In order to study the codes, we begin with studying the structure of…
The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
Interplay between coding theory and combinatorial $t$-designs has been a hot topic for many years for combinatorialists and coding theorists. Some infinite families of cyclic codes supporting infinite families of $3$-designs have been…
Based on a generic construction, two classes of ternary three-weight linear codes are obtained from a family of power functions, including some APN power functions. The weight distributions of these linear codes are determined through…
We propose a unified theory of generalized weights for linear codes endowed with an arbitrary distance. Instead of relying on supports or anticodes, the weights of a code are defined via the intersections of the code with a chosen family of…