Indian Journal of Pure and Applied Mathematics | 2021
A class of constacyclic codes over $${\\mathbb{F}}_{p^m}[u]/\\left\\langle u^2\\right\\rangle$$
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]/\\left $ 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 $R.$