arXiv subjects
Publications and source records attributed to Samir Assuena.
In this paper, we shall study k-Galois LCD constacyclic group codes over finite commutative chain rings with identity. In particular, we shall characterize Galois LCD constacyclic codes over finite commutative chain ring with identity in terms of its idempotent generators and the classical involution using the twisted group ring structures and find some good LCD codes.
In this paper, we shall give an explicit proof that constacyclic codes over finite commutative rings can be realized as ideals in some twisted group rings. Also, we shall study isometries between those codes and, finally, we shall study k-Galois LCD constacyclic codes over finite fields. In particular, we shall characterize constacyclic LCD codes with respect to Euclidean inner product in terms of its idempotent generators and the classical involution using the twisted group algebras structures and find some good LCD codes.
We give a simple construction of codes from left ideals in group algebras of certain dihedral groups and give an example to show that they can produce codes with weights equal to those of the best known codes of the same length.