Complete classification of repeated-root s-constacyclic codes of prime power length over F-pm[u]/
Complete classification of repeated-root s-constacyclic codes of prime power length over F-pm[u]/
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F-pm[u]/ 上素数幂长度重根 s-常循环码的完整分类
DOI：
10.1016/j.disc.2021.112325
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发表时间：
2021
影响因子：
0.8
通讯作者：
Wang Liqi
中科院分区：
文献类型：
--
作者：
Laaouine Jamal;Charkani Mohammed Elhassani;Wang Liqi
设R= Fpm [u]是< u 3>有单位元的有限交换链环，其中p是素数，m是正整数，Fpm是有pm个元的有限域.本文研究R上长度为ps的σ-常循环码，即环R [x] scin <xps − σ>的理想，其中σ是域Fpm的非零元素.首先，我们对R上所有长度为ps的循环码进行分类，并得到每类循环码的码字个数。进一步，利用环同构完全确定了R上长为ps的σ-常循环码的结构.
Let R= F p m [u]∕< u 3> be the finite commutative chain ring with unity, where p is a prime, m is a positive integer and F p m is a finite field with p m elements. In this study, we investigate σ-constacyclic codes of length p s over R, that is, ideals of the ring R [x]∕< x p s− σ>, where σ is a nonzero element of the field F p m. First, we classify all cyclic codes of length p s over R and obtain the number of codewords in each type of those cyclic codes. Furthermore, by using the ring isomorphism we completely determine the structure of σ-constacyclic codes of length p s over R.