Related papers: A new approach to construct minimal linear codes o…
Linear codes over finite fields parameterized by functions have proven to be a powerful tool in coding theory, yielding optimal and few-weight codes with significant applications in secret sharing, authentication codes, and association…
Algorithms to construct minimal left group codes are provided. These are based on results describing a complete set of orthogonal primitive idempotents in each Wedderburn component of a semisimple finite group algebra FG for a large class…
We consider a new class of linear codes, called affine Grassmann codes. These can be viewed as a variant of generalized Reed-Muller codes and are closely related to Grassmann codes. We determine the length, dimension, and the minimum…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
Three classes of binary linear codes with at most four nonzero weights were constructed in this paper, in which two of them are projective three-weight codes. As applications, $s$-sum sets for any odd $ s > 1$ were constructed.
A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the…
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…
Recently, linear codes constructed from defining sets have been studied extensively. They may have nice parameters if the defining set is chosen properly. Let $ m >2$ be a positive integer. For an odd prime $ p $, let $ r=p^m $ and…
For any positive integer $m$ and an odd prime $p$; let $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $q=p^{m}$, be a ring extension of the ring $\mathbb{F}_{p}+u\mathbb{F}_{p}.$ In this paper, we construct linear codes over…
Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight Griesmer $[\frac{q^k-1}{q-1},k…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
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,…
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…
In this paper, we give a geometric characterization of minimal linear codes. In particular, we relate minimal linear codes to cutting blocking sets, introduced in a recent paper by Bonini and Borello. Using this characterization, we derive…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…
In this paper, a class of two-weight and three-weight linear codes over $\gf(p)$ is constructed, and their application in secret sharing is investigated. Some of the linear codes obtained are optimal in the sense that they meet certain…
In this paper, we apply two-to-one functions over $\mathbb{F}_{2^n}$ in two generic constructions of binary linear codes. We consider two-to-one functions in two forms: (1) generalized quadratic functions; and (2) $\left(x^{2^t}+x\right)^e$…
Linear codes with few weights have applications in authentication codes, secrete sharing schemes, association schemes, consumer electronics and data storage system. In this paper, several classes of linear codes with two or three weights…
We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of…