Skew constacyclic codes over finite commutative semi-simple rings
Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 419-437
https://doi.org/10.4134/BKMS.b180314
Published online 2019 Mar 01
Hai Q. Dinh, Bac Trong Nguyen, Songsak Sriboonchitta
Ton Duc Thang University; Thai Nguyen University; 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 ${\bf F}_i$'s are finite fields. The structures of skew $\lambda$-constacyclic codes over finite commutative semi-simple rings and their duals are provided. Moreover, skew $\lambda$-constacyclic codes of arbitrary length are studied under a new definition. We also show that 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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