Further results on optimal ternary cyclic codes
Further results on optimal ternary cyclic codes
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关于最优三进制循环码的进一步结果
DOI：
10.1016/j.ffa.2021.101898
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发表时间：
2021
影响因子：
1
通讯作者：
Xiwang Cao
中科院分区：
文献类型：
--
作者：
Zhengbang Zha;Lei Hu;Yan Liu;Xiwang Cao
设C(u，v)表示具有两个非零点αu和αv的三进制循环码，其中α是F3 m⁎和0≤u，v≤3 m−2的生成元。本文给出了C(u，v)是最优三进循环码的一个充分条件。在此基础上，通过选取合适的u和v，得到了几类最优的三值循环码，并证明了C(3m+1 2，3m−1 2+v)和C(1，v)具有相同的最优性。
Let C (u, v) denote the ternary cyclic code with two nonzeros α u and α v, where α is a generator of F 3 m⁎ and 0≤ u, v≤ 3 m− 2. In this paper, we present a sufficient condition such that C (u, v) is an optimal ternary cyclic code. Based on this condition, we get several classes of optimal ternary cyclic codes by choosing the proper u and v. Moreover, we show that C (3 m+ 1 2, 3 m− 1 2+ v) and C (1, v) have the same optimality.