Cyclic codes with few weights and Niho exponents
Cyclic codes with few weights and Niho exponents
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DOI：
10.1016/j.jcta.2004.07.001
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发表时间：
2004-11
期刊：
影响因子：
--
通讯作者：
P. Charpin
中科院分区：
文献类型：
--
作者：
P. Charpin
本文研究了Tr是[公式：见正文]上的迹函数，m= 2 t，gcd（2 m-1，k）=1的和的值.我们主要证明了当k <$2j（mod 2 t-1）时，对于某个j，当a通过[公式：见正文]时，Sk（a）至少取4个值.这一结果和其他导出的性质，可以在一些循环码的权重和m序列的互相关函数的研究中看到。
This paper studies the values of the sums where Tr is the trace function on [Formula: see text] , m=2t and gcd(2m-1,k)=1. We mainly prove that when k≡2j(mod2t-1), for some j, then Sk(a) takes at least four values when a runs through [Formula: see text] . This result, and other derived properties, can be viewed in the study of weights of some cyclic codes and of crosscorrelation function of m-sequences.