Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2020; 57(2): 459-479

Online first article December 17, 2019      Printed March 31, 2020

https://doi.org/10.4134/BKMS.b190325

Copyright © The Korean Mathematical Society.

On generalizations of skew quasi-cyclic codes

Sumeyra Bedir, Fatmanur Gursoy, Irfan Siap

Yildiz Technical University; Yildiz Technical University; Jacodesmath Institute

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.

Keywords: Skew cyclic codes, skew quasi-cyclic codes, generalized quasi-cyclic codes, multi-twisted codes, polycyclic codes

MSC numbers: Primary 94B05, 94B60, 11T71

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