New informations on the structure of the functional codes defined by forms of degree $h$ on non-degenerate Hermitian varieties in $\mathbb{P}^{n(\mathbb{F}_q)$}
| Autor: | Edoukou, Frédéric A. B., Ling, San, Xing, Chaoping |
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| Rok vydání: | 2009 |
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| Druh dokumentu: | Working Paper |
| Popis: | We study the functional codes of order $h$ defined by G. Lachaud on $\mathcal{X} \subset {\mathbb{P}}^n(\mathbb{F}_q)$ a non-degenerate Hermitian variety. We give a condition of divisibility of the weights of the codewords. For $\mathcal{X}$ a non-degenerate Hermitian surface, we list the first five weights and the corresponding codewords and give a positive answer on a conjecture formulated on this question. The paper ends with a conjecture on the minimum distance and the distribution of the codewords of the first $2h+1$ weights of the functional codes for the functional codes of order $h$ on $\mathcal{X} \subset {\mathbb{P}}^n(\mathbb{F}_q)$ a non-singular Hermitian variety. Comment: 12 pages |
| Databáze: | arXiv |
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