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...
| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
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2013
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| Online Access: | https://hdl.handle.net/10356/96412 http://hdl.handle.net/10220/9845 |
| _version_ | 1826127820172034048 |
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| author | Li, Chao Ling, San Qu, Longjiang |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Li, Chao Ling, San Qu, Longjiang |
| author_sort | Li, Chao |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T07:15:04Z |
| format | Journal Article |
| id | ntu-10356/96412 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:15:04Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-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 |
| 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 |
| title | 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_short | 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 |
| topic | DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory |
| url | https://hdl.handle.net/10356/96412 http://hdl.handle.net/10220/9845 |
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