Title: Skew cyclic codes of arbitrary length

Authors: Irfan Siap; Taher Abualrub; Nuh Aydin; Padmapani Seneviratne

Addresses: Department of Mathematics, Y?ld?z Technical University, Istanbul, Turkey ' Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE ' Department of Mathematics, Kenyon College, Gambier, OH, USA and Qafqaz University, Baku, Azerbaijan ' Department of Mathematics and Statistics, American University of Sharjah, Sharjah, UAE

Abstract: In this paper, we study a special type of linear codes, called skew cyclic codes, in the most general case. This set of codes is a generalisation of cyclic codes but constructed using a non-commutative ring called the skew polynomial ring. In previous works, these codes have been studied with certain restrictions on their length. This work examines their structure for an arbitrary length without any restriction. Our results show that these codes are equivalent to either cyclic codes or quasi-cyclic codes, hence establish strong connections with well-known classes of codes.

Keywords: skew cyclic codes; quasi-cyclic codes; equivalent codes; linear codes; arbitrary lengths.

DOI: 10.1504/IJICOT.2011.044674

International Journal of Information and Coding Theory, 2011 Vol.2 No.1, pp.10 - 20

Received: 07 Dec 2009
Accepted: 11 Jun 2010

Published online: 02 Jan 2012 *

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