Two Classes of Constacyclic Codes With Variable Parameters [(qm – 1)/r, k, d]
Two Classes of Constacyclic Codes With Variable Parameters [(qm – 1)/r, k, d]
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DOI：
10.1109/tit.2023.3322990
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发表时间：
2024-01
影响因子：
2.5
通讯作者：
Zhonghua Sun;C. Ding;Xiaoqiang Wang
中科院分区：
文献类型：
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作者：
Zhonghua Sun;C. Ding;Xiaoqiang Wang
有限域上的循环循环码是一族线性码，它包含循环码作为一个子类。积循环码与许多数学领域有关，在几个方面优于循环码。因此，常循环码具有重要的理论意义。另一方面，常循环码具有丰富的代数结构和高效的译码算法，在实际应用中具有重要意义。利用具有循环码的常循环码的一般构造，构造了两类常循环码。第一类常循环码由删余Dilix循环码激励，第二类恒循环码由删余广义Reed-Muller码激励。这两类常循环码包含最优线性码。本文对这两类常循环码的参数进行了分析，并提出了一些有待解决的问题。
Constacyclic codes over finite fields are a family of linear codes and contain cyclic codes as a subclass. Constacyclic codes are related to many areas of mathematics and outperform cyclic codes in several aspects. Hence, constacyclic codes are of theoretical importance. On the other hand, constacyclic codes are important in practice, as they have rich algebraic structures and may have efficient decoding algorithms. In this paper, two classes of constacyclic codes are constructed using a general construction of constacyclic codes with cyclic codes. The first class of constacyclic codes is motivated by the punctured Dilix cyclic codes and the second class is motivated by the punctured generalised Reed-Muller codes. The two classes of constacyclic codes contain optimal linear codes. The parameters of the two classes of constacyclic codes are analysed and some open problems are presented in this paper.