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Turkish Journal of Mathematics

DOI

10.3906/mat-1808-108

Abstract

For any odd prime $p$ such that $p^m \equiv 1 \pmod{4}$, the class of $\Lambda$-constacyclic codes of length $4p^s$ over the finite commutative chain ring ${\cal R}_a=\frac{\mathbb F_{p^m}[u]}{\left\langle u^a \right\rangle}=\mathbb F_{p^m} + u \mathbb F_{p^m}+ \dots + u^{a-1}\mathbb F_{p^m}$, for all units $\Lambda$ of $\mathcal R_a$ that have the form $\Lambda=\Lambda_0+u\Lambda_1+\dots+u^{a-1}\Lambda_{a-1}$, where $\Lambda_0, \Lambda_1, \dots, \Lambda_{a-1} \in \mathbb F_{p^m}$, $\Lambda_0 \,{\not=}\, 0, \, \Lambda_1 \,{\not=}\, 0$, is investigated. If the unit $\Lambda$ is a square, each $\Lambda$-constacyclic code of length $4p^s$ is expressed as a direct sum of a $-\lambda$-constacyclic code and a $\lambda$-constacyclic code of length $2p^s$. In the main case that the unit $\Lambda$ is not a square, we show that any nonzero polynomial of degree $

First Page

561

Last Page

578

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