Constacyclic codes contain cyclic codes as a subclass and have nice algebraic structures. Constacyclic codes have theoretical importance, as they are connected 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; 环球法典具有理论重要性,因为它们与若干数学领域有关,在若干方面与优于性能的环球法典有关; 环球法典是一个次类的环球法典,在许多情况下是距离最优的,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; 本文对若干代代数及其双胞胎的家族进行了构建和分析; 这些单环球法典及其双胞胎的家族含有远距离最优的法典,并且一般具有非常良好的参数。
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