On Generalizations of Skew Quasi-cyclic Codes
Bull. Korean Math. Soc.
Published online December 17, 2019
Sumeyra Bedir, Fatmanur Gursoy, and Irfan Siap
Yildiz Technical University, Jacodesmath Institute
Abstract : In the last two decades, codes over noncommutative rings have been the main trend 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
MSC numbers : 94B05, 94B60, 11T71
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