Bulletin of the
Korean Mathematical Society BKMS

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

Supported by: H. Q. Dinh and S. Sriboonchitta are grateful to the Centre of Excellence in Econometrics, Chiang Mai University, for partial nancial support. This research is partially supported by the Research Administration Centre, Chaing Mai University.