On the covering structures of two classes of linear codes from perfect nonlinear functions

On the covering structures of two classes of linear codes from perfect nonlinear functions

In this paper, the weight distributions of two classes of linear codes based on all known explicit perfect nonlinear functions from Fqm to itself are determined using a unified approach. All the minimal codewords of these codes are characterized according to their weights, which suggests that their...

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Main Authors: Li, Chao, Ling, San, Qu, Longjiang
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2013
Subjects:
DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory
Online Access:https://hdl.handle.net/10356/96412
http://hdl.handle.net/10220/9845
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-964122023-02-28T19:22:52Z On the covering structures of two classes of linear codes from perfect nonlinear functions Li, Chao Ling, San Qu, Longjiang School of Physical and Mathematical Sciences DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory In this paper, the weight distributions of two classes of linear codes based on all known explicit perfect nonlinear functions from Fqm to itself are determined using a unified approach. All the minimal codewords of these codes are characterized according to their weights, which suggests that their covering structures are determined. Finally, all the minimal access sets of the secret sharing schemes based on their dual codes are obtained. Accepted version 2013-04-22T07:50:04Z 2019-12-06T19:30:17Z 2013-04-22T07:50:04Z 2019-12-06T19:30:17Z 2009 2009 Journal Article Li, C., Ling, S., & Qu, L. (2009). On the Covering Structures of Two Classes of Linear Codes From Perfect Nonlinear Functions. IEEE Transactions on Information Theory, 55(1), 70-82. 0018-9448 https://hdl.handle.net/10356/96412 http://hdl.handle.net/10220/9845 10.1109/TIT.2008.2008145 en IEEE transactions on information theory © 2009 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.2008.2008145]. 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::Data::Coding and information theory
spellingShingle DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory
Li, Chao
Ling, San
Qu, Longjiang
On the covering structures of two classes of linear codes from perfect nonlinear functions
description In this paper, the weight distributions of two classes of linear codes based on all known explicit perfect nonlinear functions from Fqm to itself are determined using a unified approach. All the minimal codewords of these codes are characterized according to their weights, which suggests that their covering structures are determined. Finally, all the minimal access sets of the secret sharing schemes based on their dual codes are obtained.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Li, Chao
Ling, San
Qu, Longjiang
format Article
author Li, Chao
Ling, San
Qu, Longjiang
author_sort Li, Chao
title On the covering structures of two classes of linear codes from perfect nonlinear functions
title_short On the covering structures of two classes of linear codes from perfect nonlinear functions
title_full On the covering structures of two classes of linear codes from perfect nonlinear functions
title_fullStr On the covering structures of two classes of linear codes from perfect nonlinear functions
title_full_unstemmed On the covering structures of two classes of linear codes from perfect nonlinear functions
title_sort on the covering structures of two classes of linear codes from perfect nonlinear functions
publishDate 2013
url https://hdl.handle.net/10356/96412
http://hdl.handle.net/10220/9845
_version_ 1759857052876800000

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