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...
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| Main Authors: | , , |
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| 格式: | Conference or Workshop Item |
| 語言: | English |
| 出版: |
2013
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| 主題: | |
| 在線閱讀: | https://hdl.handle.net/10356/102595 http://hdl.handle.net/10220/16387 |
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| 總結: | 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. |
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