Rank weight hierarchy of some classes of cyclic codes

Rank weight hierarchy of some classes of cyclic codes

We study the rank weight hierarchy, thus in particular the rank metric, of cyclic codes over the finite field Fqm, q a prime power, m ≤ 2. We establish the rank weight hierarchy for [n, n - 1] cyclic codes and characterize [n, k] cyclic codes of rank metric 1 when (1) k = 1, (2) n and q are coprime,...

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Main Authors: Ducoat, Jérôme, Oggier, Frédérique
Other Authors: School of Physical and Mathematical Sciences
Format: Conference or Workshop Item
Language:English
Published: 2015
Subjects:
DRNTU::Science::Physics::Atomic physics::Field theories
Online Access:https://hdl.handle.net/10356/104524
http://hdl.handle.net/10220/25585
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1045242023-02-28T19:17:56Z Rank weight hierarchy of some classes of cyclic codes Ducoat, Jérôme Oggier, Frédérique School of Physical and Mathematical Sciences Information Theory Workshop (ITW), 2014 IEEE DRNTU::Science::Physics::Atomic physics::Field theories We study the rank weight hierarchy, thus in particular the rank metric, of cyclic codes over the finite field Fqm, q a prime power, m ≤ 2. We establish the rank weight hierarchy for [n, n - 1] cyclic codes and characterize [n, k] cyclic codes of rank metric 1 when (1) k = 1, (2) n and q are coprime, and (3) the characteristic char(Fq) divides n. Finally, for n and q coprime, cyclic codes of minimal r-rank are characterized, and a refinement of the Singleton bound for the rank weight is derived. Accepted version 2015-05-18T07:45:46Z 2019-12-06T21:34:29Z 2015-05-18T07:45:46Z 2019-12-06T21:34:29Z 2014 2014 Conference Paper Ducoat, J., & Oggier, F. (2014). Rank weight hierarchy of some classes of cyclic codes. Proceedings of Information Theory Workshop (ITW), 2014 IEEE, 142-146. https://hdl.handle.net/10356/104524 http://hdl.handle.net/10220/25585 10.1109/ITW.2014.6970809 en © 2014 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/ITW.2014.6970809]. 5 p. 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::Science::Physics::Atomic physics::Field theories
spellingShingle DRNTU::Science::Physics::Atomic physics::Field theories
Ducoat, Jérôme
Oggier, Frédérique
Rank weight hierarchy of some classes of cyclic codes
description We study the rank weight hierarchy, thus in particular the rank metric, of cyclic codes over the finite field Fqm, q a prime power, m ≤ 2. We establish the rank weight hierarchy for [n, n - 1] cyclic codes and characterize [n, k] cyclic codes of rank metric 1 when (1) k = 1, (2) n and q are coprime, and (3) the characteristic char(Fq) divides n. Finally, for n and q coprime, cyclic codes of minimal r-rank are characterized, and a refinement of the Singleton bound for the rank weight is derived.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Ducoat, Jérôme
Oggier, Frédérique
format Conference or Workshop Item
author Ducoat, Jérôme
Oggier, Frédérique
author_sort Ducoat, Jérôme
title Rank weight hierarchy of some classes of cyclic codes
title_short Rank weight hierarchy of some classes of cyclic codes
title_full Rank weight hierarchy of some classes of cyclic codes
title_fullStr Rank weight hierarchy of some classes of cyclic codes
title_full_unstemmed Rank weight hierarchy of some classes of cyclic codes
title_sort rank weight hierarchy of some classes of cyclic codes
publishDate 2015
url https://hdl.handle.net/10356/104524
http://hdl.handle.net/10220/25585
_version_ 1759857347116662784

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