ON GENERALIZATIONS OF SKEW QUASI-CYCLIC CODES - Bedir, Sumeyra; Gursoy, Fatmanur; Siap, Irfan (KOREAN MATHEMATICAL SOC, 2020)
In the last two decades, codes over noncommutative rings have been one of the main trends in coding theory. Due to the fact that noncommutativity brings many challenging problems in its nature, still there are many open problems to be addressed. In 2015, generator polynomial matrices and parity-check polynomial matrices of generalized quasi-cyclic (GQC) codes were investigated by Matsui. We extended these results to the noncommutative case. Exploring the dual structures of skew constacyclic codes, we present a direct way of obtaining parity-check polynomials of skew multi-twisted codes in terms of their generators. Further, we lay out the algebraic structures of skew multi-polycyclic codes and their duals and we give some examples to illustrate the theorems.
Keywords: Skew cyclic codes; skew quasi-cyclic codes; generalized quasi-cyclic codes; multi-twisted codes; polycyclic codes; TWISTED CODES; ALGEBRAIC STRUCTURE; CONSTACYCLIC CODES; Mathematics