Primitive Idempotents and Constacyclic Codes over Finite Chain Rings

Mohammed Elhassani Charkani; Joël Kabore

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arXiv · 1908.07368

Primitive Idempotents and Constacyclic Codes over Finite Chain Rings

Mohammed Elhassani Charkani·Joël Kabore

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Abstract

Let $R$ be a commutative local finite ring. In this paper, we construct the complete set of pairwise orthogonal primitive idempotents of $R[X]/ $ where $g$ is a regular polynomial in $R[X]$. We use this set to decompose the ring $R[X]/ $ and to give the structure of constacyclic codes over finite chain rings. This allows us to describe generators of the dual code $\mathcal{C}^\bot$ of a constacyclic code $\mathcal{C}$ and to characterize non-trivial self-dual constacyclic codes over finite chain rings.

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Mohammed Elhassani Charkani, Joël Kabore. 2019-08-16. Primitive Idempotents and Constacyclic Codes over Finite Chain Rings. https://arxiv.org/abs/1908.07368

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