Constacyclic codes contain cyclic codes as a subclass and have nice algebraic structures. Constacyclic codes are important in theory, as they are closely related to a number of areas of mathematics and outperform cyclic codes in several aspects. Negacyclic codes are a subclass of constacyclic codes and are distance-optimal in many cases. However, compared with the extensive study of cyclic codes, negacyclic codes are much less studied. In this paper, several families of ternary negacyclic codes and their duals are constructed and analysed. These families of negacyclic codes and their duals contain distance-optimal codes and have very good parameters in general.
翻译：环球法典作为一个亚类包含环球法典,并且具有良好的代数结构; 环球法典在理论上很重要,因为它们在许多方面与数学的一些领域密切相关,而且优于周期法典; 环球法典是一个亚类的环球法典,在许多情况下是距离最佳的,然而,与对环球法典的广泛研究相比,对中环法典的研究要少得多; 在本文中,建立并分析了若干个双胞胎的代数及其双胞胎。 这些全环法典及其双胞胎的家族含有远距离最理想的编码,并且一般具有非常良好的参数。
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