Split group codes
We construct a class of codes of length n such that the minimum distance d outside of a certain subcode is, up to a constant factor, bounded below by the square root of n, a well-known property of quadratic residue codes. The construction, using the group algebra of an Abelian group and a special pa...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2013
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| Online Access: | https://hdl.handle.net/10356/95763 http://hdl.handle.net/10220/9820 |
| _version_ | 1826126730247536640 |
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| author | Kohel, David R. Ding, Cunsheng Ling, San |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Kohel, David R. Ding, Cunsheng Ling, San |
| author_sort | Kohel, David R. |
| collection | NTU |
| description | We construct a class of codes of length n such that the minimum distance d outside of a certain subcode is, up to a constant factor, bounded below by the square root of n, a well-known property of quadratic residue codes. The construction, using the group algebra of an Abelian group and a special partition or splitting of the group, yields quadratic residue codes, duadic codes, and their generalizations as special cases. We show that most of the special properties of these codes have analogues for split group codes, and present examples of new classes of codes obtained by this construction. |
| first_indexed | 2024-10-01T06:57:07Z |
| format | Journal Article |
| id | ntu-10356/95763 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:57:07Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/957632023-02-28T19:24:32Z Split group codes Kohel, David R. Ding, Cunsheng Ling, San School of Physical and Mathematical Sciences DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory We construct a class of codes of length n such that the minimum distance d outside of a certain subcode is, up to a constant factor, bounded below by the square root of n, a well-known property of quadratic residue codes. The construction, using the group algebra of an Abelian group and a special partition or splitting of the group, yields quadratic residue codes, duadic codes, and their generalizations as special cases. We show that most of the special properties of these codes have analogues for split group codes, and present examples of new classes of codes obtained by this construction. Accepted version 2013-04-16T09:04:51Z 2019-12-06T19:21:00Z 2013-04-16T09:04:51Z 2019-12-06T19:21:00Z 2000 2000 Journal Article Ding, C., Kohel, D. R., & Ling, S. (2000). Split group codes. IEEE Transactions on Information Theory, 46(2), 485-495. 0018-9448 https://hdl.handle.net/10356/95763 http://hdl.handle.net/10220/9820 10.1109/18.825811 en IEEE transactions on information theory © 2000 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: [DOI: http://dx.doi.org/10.1109/18.825811]. application/pdf |
| spellingShingle | DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory Kohel, David R. Ding, Cunsheng Ling, San Split group codes |
| title | Split group codes |
| title_full | Split group codes |
| title_fullStr | Split group codes |
| title_full_unstemmed | Split group codes |
| title_short | Split group codes |
| title_sort | split group codes |
| topic | DRNTU::Engineering::Computer science and engineering::Data::Coding and information theory |
| url | https://hdl.handle.net/10356/95763 http://hdl.handle.net/10220/9820 |
| work_keys_str_mv | AT koheldavidr splitgroupcodes AT dingcunsheng splitgroupcodes AT lingsan splitgroupcodes |