Title :
A Family of Five-Weight Cyclic Codes and Their Weight Enumerators
Author :
Zhengchun Zhou ; Cunsheng Ding ; Jinquan Luo ; Aixian Zhang
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. In this paper, a family of p-ary cyclic codes whose duals have three pairwise nonconjugate zeros is proposed. The weight distribution of this family of cyclic codes is determined. It turns out that the proposed cyclic codes have five nonzero weights.
Keywords :
cyclic codes; linear codes; consumer electronics; data storage systems; decoding algorithms; encoding algorithms; five weight cyclic codes; linear codes; nonconjugate zeros; nonzero weights; p-ary cyclic codes; weight distribution; weight enumerators; Cryptography; Educational institutions; Generators; Linear codes; Mathematical model; Polynomials; Cyclic codes; exponential sum; quadratic form; weight distribution; weight enumerator;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2013.2267722
