论文标题
有限pir上的不可依赖的元素constacyclic代码
Non-Invertible-Element Constacyclic Codes over Finite PIRs
论文作者
论文摘要
在本文中，我们介绍了$λ$ - constacyclic代码的概念，而有限环$ r $ $ r $ $ r $的$λ$。我们研究了有限的主理想环（PIRS），研究了不可依赖的元素constacyclic代码（NIE-CONSTACYCLIC代码）。我们确定所有NIE-Constacyclic代码在有限链环上的代数结构，给出定义多项式集合的独特形式，并获得其最小锤距。还提供了在有限链环上的Nie-Constacyclic代码双重形式的一般形式。特别是，我们为Nie-Constacyclic代码的双重二重性提供了必要和充分的条件，使其成为NIE-Constacyclic代码。使用中国的剩余定理，我们研究了有限的PIRS的NIE-CONSTACYCLIC代码。此外，我们在有限的pir上构建了一些最佳的NIE-CONSTACYCLIC代码，因为它们可以在某些给定的长度和基础上实现最大可能的最小锤距。
In this paper we introduce the notion of $λ$-constacyclic codes over finite rings $R$ for arbitary element $λ$ of $R$. We study the non-invertible-element constacyclic codes (NIE-constacyclic codes) over finite principal ideal rings (PIRs). We determine the algebraic structures of all NIE-constacyclic codes over finite chain rings, give the unique form of the sets of the defining polynomials and obtain their minimum Hamming distances. A general form of the duals of NIE-constacyclic codes over finite chain rings is also provided. In particular, we give a necessary and sufficient condition for the dual of an NIE-constacyclic code to be an NIE-constacyclic code. Using the Chinese Remainder Theorem, we study the NIE-constacyclic codes over finite PIRs. Furthermore, we construct some optimal NIE-constacyclic codes over finite PIRs in the sense that they achieve the maximum possible minimum Hamming distances for some given lengths and cardinalities.
