On the algebraic structure of quasi-cyclic codes III : generator theory

On the algebraic structure of quasi-cyclic codes III : generator theory

Following Parts I and II, quasi-cyclic codes of given index are studied as codes over a finite polynomial ring. These latter codes are decomposed by the Chinese Remainder Theorem (CRT), or equivalently the Mattson-Solomon transform, into products of shorter codes over larger alphabets. We characteri...

Full description

Saved in:
Bibliographic Details
Main Authors: Ling, San, Sole, Patrick
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2013
Subjects:
DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation
Online Access:https://hdl.handle.net/10356/96414
http://hdl.handle.net/10220/9826
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-96414
record_format dspace
spelling sg-ntu-dr.10356-964142023-02-28T19:22:51Z On the algebraic structure of quasi-cyclic codes III : generator theory Ling, San Sole, Patrick School of Physical and Mathematical Sciences DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation Following Parts I and II, quasi-cyclic codes of given index are studied as codes over a finite polynomial ring. These latter codes are decomposed by the Chinese Remainder Theorem (CRT), or equivalently the Mattson-Solomon transform, into products of shorter codes over larger alphabets. We characterize and enumerate self-dual one-generator quasi-cyclic codes in that context. We give an algorithm to remove some equivalent codes from that enumeration. A generalization to multigenerator codes is sketched. Accepted version 2013-04-18T04:19:35Z 2019-12-06T19:30:20Z 2013-04-18T04:19:35Z 2019-12-06T19:30:20Z 2005 2005 Journal Article Ling, S., & Solé, P. (2005). On the Algebraic Structure of Quasi-Cyclic Codes III: Generator Theory. IEEE Transactions on Information Theory, 51(7), 2692-2700. 0018-9448 https://hdl.handle.net/10356/96414 http://hdl.handle.net/10220/9826 10.1109/TIT.2005.850142 en IEEE transactions on information theory © 2005 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: [http://dx.doi.org/10.1109/TIT.2005.850142]. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation
spellingShingle DRNTU::Engineering::Computer science and engineering::Computing methodologies::Symbolic and algebraic manipulation
Ling, San
Sole, Patrick
On the algebraic structure of quasi-cyclic codes III : generator theory
description Following Parts I and II, quasi-cyclic codes of given index are studied as codes over a finite polynomial ring. These latter codes are decomposed by the Chinese Remainder Theorem (CRT), or equivalently the Mattson-Solomon transform, into products of shorter codes over larger alphabets. We characterize and enumerate self-dual one-generator quasi-cyclic codes in that context. We give an algorithm to remove some equivalent codes from that enumeration. A generalization to multigenerator codes is sketched.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Ling, San
Sole, Patrick
format Article
author Ling, San
Sole, Patrick
author_sort Ling, San
title On the algebraic structure of quasi-cyclic codes III : generator theory
title_short On the algebraic structure of quasi-cyclic codes III : generator theory
title_full On the algebraic structure of quasi-cyclic codes III : generator theory
title_fullStr On the algebraic structure of quasi-cyclic codes III : generator theory
title_full_unstemmed On the algebraic structure of quasi-cyclic codes III : generator theory
title_sort on the algebraic structure of quasi-cyclic codes iii : generator theory
publishDate 2013
url https://hdl.handle.net/10356/96414
http://hdl.handle.net/10220/9826
_version_ 1759854701469237248

Similar Items