A class of constacyclic codes over ${\mathbb{F}}_{p^m}[u]/⟨u^2⟩$

Abstract

Let $p$ be an odd prime, and let $m$ be a positive integer satisfying $p^m\equiv 3(\text{mod }4).$ Let ${\mathbb{F}}_{p^m}$ be the finite field with $p^m$ elements, and let $R={\mathbb{F}}_{p^m}[u]/⟨u^2⟩$ be the finite commutative chain ring with unity. In this paper, we determine all constacyclic codes of length $4p^s$ over $R$ and their dual codes, where $s$ is a positive integer. We also determine their sizes and list some isodual constacyclic codes of length $4p^s$ over $R.$

Cited by in corpus (2)

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