Please use this identifier to cite or link to this item:
Title: Novel Indexing of Cyclic Codes with Run-Length Applications
Authors: Hai Q. Dinh
Ramy Taki Eldin
Jirakom Sirisrisakulchai
Keywords: Computer Science
Materials Science
Issue Date: 1-Jan-2019
Abstract: © 2013 IEEE. Any cyclic code over a finite field can be considered as a sum of some non-degenerate irreducible cyclic codes. We use the traditional trace function representation of irreducible cyclic codes to suggest a similar representation to any cyclic code. This representation suggests an indexing for codewords of the cyclic code. Specifically, each codeword is identified by a triplet IA,RA and QA. The relationship between these triplets was studied for codewords that are cyclic shifts of each other. We introduce a set SC whose elements correspond to subsets that each contains all the cyclic shifts of a codeword. As an application to the proposed indexing, we take advantage of the trace function linearity to explore codewords with a specific run-length. Because the run-length is invariant to cyclic shifts, it suffices to explore elements of SC that match codewords with a specific run-length. Instead of searching at the code for these codewords, the problem is turned into solving a system of linear equations.
ISSN: 21693536
Appears in Collections:CMUL: Journal Articles

Files in This Item:
There are no files associated with this item.

Items in CMUIR are protected by copyright, with all rights reserved, unless otherwise indicated.