Related papers: On linear codes and distinct weights
In this paper, we continue the study of linear sets with complementary weights. We find criteria to determine the set of points of any fixed weight and use this to present particular linear sets with few points of weight more than one. We…
Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to…
We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main…
Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime $p$, we propose a class of $p$-ary linear codes by choosing a proper defining set.…
Combinatorial designs are closely related to linear codes. In recent year, there are a lot of $t$-designs constructed from certain linear codes. In this paper, we aim to construct $2$-designs from binary three-weight codes. For any binary…
Usually, it is difficult to determine the weight distribution of an irreducible cyclic code. In this paper, we discuss the case when an irreducible cyclic code has the maximal number of distinct nonzero weights and give a necessary and…
Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, we determined the complete weight enumerator of two classes of p-ary linear codes constructed from defining set.…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes…
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association…
Linear codes have been an interesting subject of study for many years. Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, a class of three-weight linear codes over Fp…
In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code.…
We first establish a simple yet powerful necessary and sufficient condition for a binary linear code to be SO, leading to a complete characterization of singly-even codes in this family. We further derive necessary and sufficient conditions…
We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of…
In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.
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…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
In this paper, we study one-Lee weight and two-Lee weight codes over $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$, where $u^{2}=0$. Some properties of one-Lee weight $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-additive codes are given, and a complete…
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime $p$, we determine the explicit complete weight enumerators of two classes of linear codes over $\mathbb{F}_p$ and they…
In this paper, on one hand, a class of linear codes with one or two weights is obtained. Based on these linear codes, we construct two classes of constant composition codes, which includes optimal constant composition codes depending on…