Weight enumerators of reducible cyclic codes and their dual codes
Weight enumerators of reducible cyclic codes and their dual codes
复制标题
可约化循环码及其对偶码的权重枚举器
DOI：
10.1016/j.disc.2018.10.035
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发表时间：
2019
影响因子：
0.8
通讯作者：
Yang Shudi
中科院分区：
文献类型：
--
作者：
Wu Yansheng;Yue Qin;Zhu Xiaomeng;Yang Shudi
设Fq为有限域，n为正整数.本文给出了一种新的组合方法来确定Fq上长度为n的可约循环码及其对偶码的重量计数元，推广了Zhu等人的结果.（2015）;特别地，我们还给出了循环码的重量计数器，它被视为部分Melas码。此外，本文得到的权枚举数都是多项式幂的形式。
Let F q be a finite field and n a positive integer. In this paper, we find a new combinatorial method to determine weight enumerators of reducible cyclic codes and their dual codes of length n over F q, which just generalize results of Zhu et al.(2015); especially, we also give the weight enumerator of a cyclic code, which is viewed as a partial Melas code. Furthermore, weight enumerators obtained in this paper are all in the form of power of a polynomial.