Self-Dual Skew Cyclic Codes over F_q+uF_q
share
In this paper, we give conditions for the existence of Hermitian self-dual 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_q^2, 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 BF3 to construct self-dual skew cyclic codes based on the least common left multiples of non-commutative polynomials over F_q+uF_q.
READ FULL TEXT