Related papers: The Structure of One Weight Linear and Cyclic Code…
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…
A cyclic codes of length $n$ over the rings $Z_{2^{m}}$ of integer of modulo $2^{m}$ is a linear code with property that if the codeword $(c_0,c_1,...,c_{n-1})\in \mathcal{C}$ then the cyclic shift $(c_1,c_2,...,c_0)\in \mathcal{C}$.…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Cyclic codes have been studied for many years, but their weight…
Linear codes are considered over the ring $\mathbb{Z}_4+v\mathbb{Z}_4$, where $v^2=v$. Gray weight, Gray maps for linear codes are defined and MacWilliams identity for the Gray weight enumerator is given. Self-dual codes, construction of…
Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…
Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…
We investigate linear codes over the ring $\mathbb{Z}_4 + u\mathbb{Z}_4 + v\mathbb{Z}_4 + w\mathbb{Z}_4 + uv\mathbb{Z}_4 + uw\mathbb{Z}_4 + vw\mathbb{Z}_4 + uvw\mathbb{Z}_4$, with conditions $u^2=u$, $v^2=v$, $w^2=w$, $uv=vu$, $uw=wu$ and…
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…
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.
A code is said to be two-weight if the non-zero codewords have only two different a weight w1 and w2. Two-weight codes are closely related to strongly regular graphs. In this paper. It is shown that a consta-cyclic code of composite length…
Linear codes are considered over the ring Z_4+uZ_4, a non-chain extension of Z_4. Lee weights, Gray maps for these codes are defined and MacWilliams identities for the complete, symmetrized and Lee weight enumerators are proved. Two…
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…
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}…
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.…
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…
Because of efficient encoding and decoding algorithms, cyclic codes are an important family of linear block codes, and have applications in communica- tion and storage systems. However, their weight distributions are known only for a few…
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…
The objective of this paper is to construct a class of linear codes with two nonzero weights and three nonzero weights by using the general trace functions, which weight distributions has been determined. These linear codes contain some…
The rings $Z_{4}+\nu Z_{4}$ have been classified into chain rings and non-chain rings on the basis of the values of $\nu^{2} \in Z_{4}+\nu Z_{4}.$ In this paper, the structure of cyclic codes of arbitrary length over the rings $Z_{4}+\nu…
Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems due to their efficient encoding and decoding algorithms. Cyclic codes with many zeros and their…