The Weight Enumerator of Three Families of Cyclic Codes

被引:12
作者
Zhou, Zhengchun [1 ,2 ]
Zhang, Aixian [3 ]
Ding, Cunsheng [4 ]
Xiong, Maosheng [5 ]
机构
[1] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Peoples R China
[2] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
[3] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China
[4] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Kowloon, Hong Kong, Peoples R China
[5] Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China
关键词
Cyclic codes; exponential sum; Hermitian forms graphs; quadratic form; weight distribution; DISTRIBUTIONS; SEQUENCES;
D O I
10.1109/TIT.2013.2262095
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
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 dual codes have been a subject of study for many years. However, their weight distributions are known only for a very small number of cases. In general, the calculation of the weight distribution of cyclic codes is heavily based on the evaluation of some exponential sums over finite fields. Very recently, Li et al. studied a class of p-ary cyclic codes of length p(2m) - 1, where is a prime and is odd. They determined the weight distribution of this class of cyclic codes by establishing a connection between the involved exponential sums with the spectrum of Hermitian forms graphs. In this paper, this class of p-ary cyclic codes is generalized and the weight distribution of the generalized cyclic codes is settled for both even and odd along with the idea of Li et al. The weight distributions of two related families of cyclic codes are also determined.
引用
收藏
页码:6002 / 6009
页数:8
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