Please use this identifier to cite or link to this item: https://doi.org/10.1109/18.959257
Title: On the algebraic structure of quasi-cyclic codes I: Finite fields
Authors: Ling, S. 
Solé, P.
Keywords: (a + x|b + x|a + b + x) construction
(u + v|u - v) construction
(u|u + v) construction
Chinese remainder theorem (CRT)
Discrete Fourier transform (DFT)
Quasi-cyclic codes
Self-dual codes
Issue Date: Nov-2001
Citation: Ling, S., Solé, P. (2001-11). On the algebraic structure of quasi-cyclic codes I: Finite fields. IEEE Transactions on Information Theory 47 (7) : 2751-2760. ScholarBank@NUS Repository. https://doi.org/10.1109/18.959257
Abstract: A new algebraic approach to quasi-cyclic codes is introduced. The key idea is to regard a quasi-cyclic code over a field as a linear code over an auxiliary ring. By the use of the Chinese Remainder Theorem (CRT), or of the Discrete Fourier Transform (DFT), that ring can be decomposed into a direct product of fields. That ring decomposition in turn yields a code construction from codes of lower lengths which turns out to be in some cases the celebrated squaring and cubing constructions and in other cases the recent (u + v|u - v) and Vandermonde constructions. All binary extended quadratic residue codes of length a multiple of three are shown to be attainable by the cubing construction. Quinting and septing constructions are introduced. Other results made possible by the ring decomposition are a characterization of self-dual quasi-cyclic codes, and a trace representation that generalizes that of cyclic codes.
Source Title: IEEE Transactions on Information Theory
URI: http://scholarbank.nus.edu.sg/handle/10635/103766
ISSN: 00189448
DOI: 10.1109/18.959257
Appears in Collections:Staff Publications

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

SCOPUSTM   
Citations

114
checked on Oct 9, 2018

WEB OF SCIENCETM
Citations

117
checked on Oct 9, 2018

Page view(s)

36
checked on Oct 5, 2018

Google ScholarTM

Check

Altmetric


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