Seven Classes of Three-Weight Cyclic Codes

Author

Zhengchun Zhou ; Cunsheng Ding

Author_Institution

Sch. of Math., Southwest Jiaotong Univ., Chengdu, China

Volume

61

Issue

10

fYear

2013

fDate

Oct-13

Firstpage

4120

Lastpage

4126

Abstract

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms, compared with linear block codes. In this paper, seven classes of three-weight cyclic codes over gf(p) whose duals have two zeros are presented, where p is an odd prime. The weight distributions of the seven classes of cyclic codes are settled. Some of the cyclic codes are optimal in the sense that they meet certain bounds on linear codes. The application of these cyclic codes in secret sharing is also considered.

Keywords

block codes; consumer electronics; cyclic codes; decoding; linear codes; communication system; consumer electronics; data storage system; decoding algorithm; encoding algorithm; linear block code; odd prime; secret sharing; three-weight cyclic code; weight distribution; Cryptography; Educational institutions; Generators; Hamming weight; Linear code; Polynomials; Vectors; Cyclic codes; linear codes; secret sharing; weight distribution; weight enumerator;

fLanguage

English

Journal_Title

Communications, IEEE Transactions on

Publisher

ieee

ISSN

0090-6778

Type

jour

DOI

10.1109/TCOMM.2013.072213.130107

Filename

6567875