Self-Dual Skew Cyclic Codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$

Abstract

In this paper, we give conditions for the existence of Hermitian selfdual Θ−cyclic and Θ−negacyclic codes over the finite chain ring F q + uF q . By defining a Gray map from R = F q + uF q to F 2 q , we prove that the Gray images of skew cyclic codes of odd length n over R with even characteristic are equivalent to skew quasi-twisted codes of length 2n over F q of index 2. We also extend an algorithm of Boucher and Ulmer [9] to construct self-dual skew cyclic codes based on the least common left multiples of non-commutative polynomials over F q + uF q .