Linear Codes with Two or Three Weights From Quadratic Bent Functions

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed from quadratic Bent functions over the finite field \gf_p, where $p$ is an odd prime. They include some earlier linear codes as special cases. The weight distributions of these linear codes are also determined.Comment: arXiv admin note: text overlap with arXiv:1503.06512 by other author

Linear Codes With Two or Three Weights From Some Functions With Low Walsh Spectrum in Odd Characteristic

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 are obtained from some functions with low Walsh spectrum in odd characteristic. Numerical results show that some of the linear codes obtained are optimal or almost optimal in the sense that they meet certain bounds on linear codes.Comment: Some of the results of this paper are covered by others' wor

A class of linear codes with few weights

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 the linear codes obtained are optimal or almost optimal with respect to the Griesmer bound. As s applications, these linear codes can be used to construct secret sharing schemes with nice access structures

Several classes of minimal linear codes with few weights from weakly regular plateaued functions

Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many construction methods of linear codes based on functions have been proposed in the literature. In this paper, we generalize the recent construction methods given by Tang et al. in [IEEE Transactions on Information Theory, 62(3), 1166-1176, 2016] to weakly regular plateaued functions over finite fields of odd characteristic. We first construct three weight linear codes from weakly regular plateaued functions based on the second generic construction and determine their weight distributions. We next give a subcode with two or three weights of each constructed code as well as its parameter. We finally show that the constructed codes in this paper are minimal, which confirms that the secret sharing schemes based on their dual codes have the nice access structures.Comment: 31 page

The weight distributions of two classes of p ary cyclic codes with few weights

Cyclic codes have attracted a lot of research interest for decades as they have efficient encoding and decoding algorithms. In this paper, for an odd prime $p$, the weight distributions of two classes of $p$-ary cyclic codes are completely determined. We show that both codes have at most five nonzero weights.Comment: 20 page

Two classes of linear codes and their generalized Hamming weights

The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. In this paper, we investigate the generalized Hamming weights of two classes of linear codes constructed from defining sets and determine them completely employing a number-theoretic approach

On Completely Regular Codes

This work is a survey on completely regular codes. Known properties, relations with other combinatorial structures and constructions are stated. The existence problem is also discussed and known results for some particular cases are established. In particular, we present a few new results on completely regular codes with covering radius 2 and on extended completely regular codes

On the Weight Distribution of Cyclic Codes with Niho Exponents

Recently, there has been intensive research on the weight distributions of cyclic codes. In this paper, we compute the weight distributions of three classes of cyclic codes with Niho exponents. More specifically, we obtain two classes of binary three-weight and four-weight cyclic codes and a class of nonbinary four-weight cyclic codes. The weight distributions follow from the determination of value distributions of certain exponential sums. Several examples are presented to show that some of our codes are optimal and some have the best known parameters

Three-Weight Ternary Linear Codes from a Family of Monomials

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 studying the properties of some exponential sum related to the proposed power functions

Higher weight distribution of linearized Reed-Solomon codes

Linearized Reed-Solomon codes are defined. Higher weight distribution of those codes are determined