Title :
Seven Classes of Three-Weight Cyclic Codes
Author :
Zhengchun Zhou ; Cunsheng Ding
Author_Institution :
Sch. of Math., Southwest Jiaotong Univ., Chengdu, China
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;
Journal_Title :
Communications, IEEE Transactions on
DOI :
10.1109/TCOMM.2013.072213.130107
