Skew Constacyclic Codes Over Finite Commutative Semi-Simple Rings
Bull. Korean Math. Soc.
Published online 2019 Mar 15
Hai Q Dinh, Bac Trong Nguyen, and Songsak Sriboonchitta
Department of Mathematical Sciences, Kent State University, Faculty of Economics, Chiang Mai University
Abstract : This paper investigates skew $\Theta$-$\lambda$-constacyclic codes over $R={\bf F}_0\oplus {\bf F}_1 \oplus \cdots \oplus {\bf F}_{k-1}$, where ${\bf F}_i$ are finite fields. The structures of skew $\lambda$-constacyclic codes and their duals are provided. Moreover, skew $\lambda$-constacyclic codes of arbitrary length are studied. By Theorem 5.12, a skew cyclic code of arbitrary length over finite commutative semi-simple rings is equivalent to either a cyclic code over $R$ or a quasi-cyclic code over $R$.
Keywords : Cyclic codes, constacyclic codes, dual codes, skew $\Theta$-cyclic codes, skew $\Theta$-negacyclic codes, skew $\Theta$-$\lambda$-constacyclic codes.
MSC numbers : Primary 94B15, 94B05; Secondary 11T71
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