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On generalizations of skew quasi-cyclic codes

Sumeyra Bedir|Fatmanur Gursoy|Irfan Siap
대한수학회 (The Korean Mathematical Society)|2020.03|대한수학회보 (Bulletin of the KMS)|제57권 제2호|pp. 459-479|DOI 10.4134/BKMS.b190325

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키워드

Skew cyclic codesskew quasi-cyclic codesgeneralized quasi-cyclic codesmulti-twisted codespolycyclic codes
주제분류수학

초록

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.

Abstract

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.

참고문헌 (35)

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