论文标题
具有可变参数的两类constacyclic代码
Two Classes of Constacyclic Codes with Variable Parameters
论文作者
论文摘要
有限字段上的constacyclic代码是线性代码的家族，并包含循环代码作为子类。 Constacyclic代码与数学的许多领域有关，并且在几个方面都超越了周期性代码。因此，constacyclic代码具有理论上的重要性。另一方面，Constacyclic代码在实践中很重要，因为它们具有丰富的代数结构，并且可能具有有效的解码算法。在本文中，使用具有循环代码的constacyclic代码的一般结构来构建两类的constacyclic代码。第一类Constacyclic代码是由刺穿的DiLix Cyclic Codes激励的，第二类是由刺穿的广义芦苇毛刺代码激励的。两类的constacyclic代码包含最佳线性代码。分析了两类constacyclic代码的参数，并在本文中提出了一些开放问题。
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.
