${\Theta }_S-$cyclic codes over $A_k$

Abstract

We study ${\Theta }_S-$cyclic codes over the family of rings $A_k.$ We characterize ${\Theta }_S-$cyclic codes in terms of their binary images. A family of Hermitian inner-products is defined and we prove that if a code is ${\Theta }_S-$cyclic then its Hermitian dual is also ${\Theta }_S-$cyclic. Finally, we give constructions of ${\Theta }_S-$cyclic codes.

23 pages