Construction and enumeration for self-dual cyclic codes of even length over F_{2^m}+uF_{2^m}
Construction and enumeration for self-dual cyclic codes of even length over F_{2^m}+uF_{2^m}
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F_2m uF_2m以上偶数自对偶循环码的构造与枚举
DOI：
10.1016/j.ffa.2019.101598
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发表时间：
2020
影响因子：
1
通讯作者：
Ma Fanghui
中科院分区：
文献类型：
--
作者：
Cao Yuan;Cao Yonglin;Dinh Hai Q.;Fu Fang-Wei;Ma Fanghui
设F2 m是基数为2 m的有限域，R= F2 m+ uF 2 m（u2 = 0），s，n是正整数，n是奇数.本文给出了长度为2sn的有限链环R上的自对偶循环码的一个显式表示，并给出了一种计算方法，从而得到了所有不同的循环码.此外，我们得到了一个明确的公式来计算所有这些自对偶循环码的数目。作为应用，从R上长度为2s + 1 n的自对偶循环码出发，通过保持R到F2 m2的正交性和距离的Gray映射，得到了F2 m上长度为2s + 1 n的自对偶和2-拟循环码.
Let F 2 m be a finite field of cardinality 2 m, R= F 2 m+ u F 2 m (u 2= 0) and s, n be positive integers such that n is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite chain ring R of length 2 s n and provide a calculation method to obtain all distinct codes. Moreover, we obtain a clear formula to count the number of all these self-dual cyclic codes. As an application, self-dual and 2-quasi-cyclic codes over F 2 m of length 2 s+ 1 n can be obtained from self-dual cyclic code over R of length 2 s n and by a Gray map preserving orthogonality and distances from R onto F 2 m 2.