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 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 Full-Text :