Related papers: Constant composition codes derived from linear cod…
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…
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…
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,…
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…
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distribution and the parameters of families of minimal codes…
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…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…
Inspired by the Z2Z4-additive codes, linear codes over Z2^r x(Z2+uZ2)^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z2^r x(Z2+uZ2)^s have some advantages…
In this paper, a family of five-weight reducible cyclic codes is presented. Furthermore, the weight distribution of these cyclic codes is determined, which follows from the determination of value distributions of certain exponential sums.
Linear codes with few weights have significant applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. There are a number of methods to construct linear codes, one of which is based on…
In this manuscript, we construct a class of projective three-weight linear codes and two classes of projective four-weight linear codes over F2 from the defining sets construction, and determine their weight distributions by using additive…
A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.
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 are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, \cite{Y-X-D12}…
A family of $\omega$-circulant balanced weighing matrices with classical parameters is used for the construction of optimal constant weight codes over an alphabet of size $g+1$ and length $n=(q^m -1)/(q-1)$, where $q$ is an odd prime power,…
Linearized Reed-Solomon codes are defined. Higher weight distribution of those codes are determined.
We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they are at most three-weight codes and they are suitable for applications…
The problem of finding good linear codes for joint source-channel coding (JSCC) is investigated in this paper. By the code-spectrum approach, it has been proved in the authors' previous paper that a good linear code for the authors' JSCC…