Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices
In this article we construct an infinite family of linear error correcting codes over Fq for any prime power q. The code parameters are [q2t + qt-1 - q2t-1 - qt, 2t+1, q2t + q2t-2 + qt-1 - 2q2t-1 - qt]q, for any positive integer t. This family is a generalisation of the optimal self-complementary bi...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Conference Paper |
| Language: | English |
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2013
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| Online Access: | https://hdl.handle.net/10356/102595 http://hdl.handle.net/10220/16387 |
| _version_ | 1811686749917675520 |
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| author | Bracken, Carl Chee, Yeow Meng Purkayastha, Punarbasu |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Bracken, Carl Chee, Yeow Meng Purkayastha, Punarbasu |
| author_sort | Bracken, Carl |
| collection | NTU |
| description | In this article we construct an infinite family of linear error correcting codes over Fq for any prime power q. The code parameters are [q2t + qt-1 - q2t-1 - qt, 2t+1, q2t + q2t-2 + qt-1 - 2q2t-1 - qt]q, for any positive integer t. This family is a generalisation of the optimal self-complementary binary codes with parameters [2u2 - u, 2t + 1, u2 - u]2, where u = 2t-1. The codes are obtained by considering a submatrix of a specially constructed generalised Hadamard matrix. The optimality of the family is confirmed by using a recently derived generalisation of the Grey-Rankin bound when t >; 1, and the Griesmer bound when t = 1. |
| first_indexed | 2024-10-01T05:05:22Z |
| format | Conference Paper |
| id | ntu-10356/102595 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:05:22Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/1025952020-03-07T12:31:20Z Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices Bracken, Carl Chee, Yeow Meng Purkayastha, Punarbasu School of Physical and Mathematical Sciences IEEE International Symposium on Information Theory (2012 : Cambridge, US) DRNTU::Science::Mathematics In this article we construct an infinite family of linear error correcting codes over Fq for any prime power q. The code parameters are [q2t + qt-1 - q2t-1 - qt, 2t+1, q2t + q2t-2 + qt-1 - 2q2t-1 - qt]q, for any positive integer t. This family is a generalisation of the optimal self-complementary binary codes with parameters [2u2 - u, 2t + 1, u2 - u]2, where u = 2t-1. The codes are obtained by considering a submatrix of a specially constructed generalised Hadamard matrix. The optimality of the family is confirmed by using a recently derived generalisation of the Grey-Rankin bound when t >; 1, and the Griesmer bound when t = 1. 2013-10-10T06:00:26Z 2019-12-06T20:57:17Z 2013-10-10T06:00:26Z 2019-12-06T20:57:17Z 2012 2012 Conference Paper Bracken, C., Chee, Y. M., & Purkayastha, P. (2012). Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices. 2012 IEEE International Symposium on Information Theory - ISIT, pp.116-119. https://hdl.handle.net/10356/102595 http://hdl.handle.net/10220/16387 10.1109/ISIT.2012.6283038 en |
| spellingShingle | DRNTU::Science::Mathematics Bracken, Carl Chee, Yeow Meng Purkayastha, Punarbasu Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices |
| title | Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices |
| title_full | Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices |
| title_fullStr | Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices |
| title_full_unstemmed | Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices |
| title_short | Optimal family of q-ary codes obtained from a substructure of generalised Hadamard matrices |
| title_sort | optimal family of q ary codes obtained from a substructure of generalised hadamard matrices |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/102595 http://hdl.handle.net/10220/16387 |
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