Recent progress on weight distributions of cyclic codes over finite fields

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Hai Q. Dinh¹  Chengju Li²  Qin Yue² 

[1] Departments of Mathematical Sciences, Kent State University;Department of Mathematics, Nanjing University of Aeronautics and Astronautics

关键词: Linear codes;    Weight distribution;    Cyclic codes;    Finite fields;    Gauss periods;    Gauss sums;    Exponential sums;    Quadratic forms;   

DOI  :  10.13069/jacodesmath.36866

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

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. In coding theory it is often desirable to know the weight distribution of a cyclic code to estimate the error correcting capability and error probability. In this paper, we present the recent progress on the weight distributions of cyclic codes over finite fields, which had been determined by exponential sums. The cyclic codes with few weights which are very useful are discussed and their existence conditions are listed. Furthermore, we discuss the more general case of constacyclic codes and give some equivalences to characterize their weight distributions.

【 授权许可】

CC BY