Skew cyclic codes of arbitrary length. (1st January 2011)

• Record Type: Journal Article
• Authors: Siap, Irfan; Abualrub, Taher; Aydin, Nuh; Seneviratne, Padmapani
• Is Part Of: International journal of information and coding theory. Volume 2:Number 1(2011)
• Page Start: 10
• Page End: 20
• Publication Date: 2011-01-01
• Subjects: cyclic codes -- skew cyclic codes -- quasi-cyclic codes -- equivalent codes; Coding theory -- Periodicals; Information theory -- Periodicals; 003.54
• Languages: English
• ISSNs: 1753-7703

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.