Multi-Symbol Distance Distributions of Repeated-Root Constacylic Codes of Prime Power Lengths

发布时间：2021-05-24 作者：浏览次数：

Speaker:	Hai Q. Dinh	DateTime:	2021年5月28日（周五）上午10:00-11:00
Brief Introduction to Speaker:		Place:	在线会议（会议号请联系刘宏伟老师获取）
Abstract:Let $p$ be an odd prime, $s$ and $m$ be positive integers and $\lambda$ be a nonzero element of $\mathbb{F}_{p^m}$. The $\lambda$-constacyclic codes of length $p^s$ over $\mathbb{F}_{p^m}$ are linearly ordered under set theoretic inclusion as ideals of the chain ring $\mathbb{F}_{p^m}[x]/\langle x^{p^s}-\lambda \rangle$. First of all, using this structure, the symbol-pair and symbol-triple distances of all such $\lambda-$constacyclic codes are established in this talk. All maximum distance separable symbol-pair and symbol-triple constacyclic codes of length $p^s$ are also determined as an application. We will discuss possible generalizations of these concepts to the most general case of multi-symbol constacylic codes and longer code lengths.