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A Note on Skew Cyclic Codes over a Class of Rings

Authors: 

Hai Q. Dinh, Bac T. Nguyen, Songsak Sriboonchitta

Source title: 
Algebra Colloquium, 27(4): 703-712, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

We study skew cyclic codes over a class of rings R=F0⊕F1⊕⋯⊕Ft−1, where each Fi(= 0,…,− 1) is a finite field. We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R. Moreover, we discuss possible extension of our results in the more general setting of δR-dual skew constacyclic codes over R, where δR is an automorphism of R.