Repeated-root constacyclic codes over finite commutative chain rings and their distances

Abstract

Let ${\mathcal{R}}_e$ be a finite commutative chain ring with nilpotency index $e\ge 2.$ In this paper, all repeated-root constacyclic codes of arbitrary lengths over ${\mathcal{R}}_2,$ their sizes and their dual codes are determined. As an application, some isodual constacyclic codes over ${\mathcal{R}}_2$ are also listed. Moreover, Hamming distances, Rosenbloom-Tsfasman distances and Rosenbloom-Tsfasman weight distributions of all repeated-root constacyclic codes over ${\mathcal{R}}_2$ and some repeated-root constacyclic codes over ${\mathcal{R}}_e$ are determined.

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• Repeated-root constacyclic codes over the finite chain ring ${\mathbb{F}}_{{\mathbf{p}}^{\mathbf{m}}}[\mathbf{u}]/⟨{\mathbf{u}}^3⟩$