Related papers: Linear Codes from a Generic Construction
A characterization of a class of optimal three-weight cyclic codes of dimension 3 over any finite field was recently presented in [10]. Shortly after this, a generalization for the sufficient numerical conditions of such characterization…
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…
In this paper, for an odd prime $p$, several classes of two-weight linear codes over the finite field $\mathbb{F}_p$ are constructed from the defining sets, and then their complete weight distributions are determined by employing character…
Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…
The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the…
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…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is…
Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two…
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…
Recently, much progress has been made to construct minimal linear codes due to their preference in secret sharing schemes and secure two-party computation. In this paper, we put forward a new method to construct minimal linear codes by…
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…
In this article we present a class of codes with few weights arising from special type of linear sets. We explicitly show the weights of such codes, their weight enumerator and possible choices for their generator matrices. In particular,…
Bounds on linear codes play a central role in coding theory, as they capture the fundamental trade-off between error-correction capability (minimum distance) and information rate (dimension relative to length). Classical results…
In this paper, we will give the generic construction of a binary linear code of dimension $n+3$ and derive the necessary and sufficient conditions for the constructed code to be minimal. Using generic construction, a new family of minimal…
It is well-known that few-weight linear codes have better applications in secret sharing schemes \cite{JY2006,CC2005}.In particular, projective two-weight codes are very precious as they are closely related to finite projective spaces,…
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, a class of $q$-ary linear codes with few weights are presented and their weight distributions are determined using Gauss periods. Some of…
Two general constructions of linear codes with functions over finite fields have been extensively studied in the literature. The first one is given by $\mathcal{C}(f)=\left\{ {\rm Tr}(af(x)+bx)_{x \in \mathbb{F}_{q^m}^*}: a,b \in…
We will show how to obtain a linear code from a configuration of affine lines in general position and a suitable set of rational points. We will also explain a new decoding algorithm based on the configuration, which seems to be quite…