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.
翻译：有关有限领域的统合法典是一套线性法典,包含作为子类的环化法典。统合法典涉及数学和超优性周期法典的许多领域,因此,共合法典具有理论重要性。另一方面,共合法典在实践上很重要,因为它们拥有丰富的代数结构,并可能具有有效的解码算法。在本文件中,两类共合法典的构建采用带有环化法典的统合法典。第一类共合法典的驱动力是穿刺的帝力周期法典,第二类由穿刺的通用Reed-Muller法典驱动。两类共合法典包含最佳线性法典。分析了两类共合法典的参数,并在本文中介绍了一些公开的问题。
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