Codes and Gap Sequences of Hermitian Curves
| Autor: | Gábor Korchmáros, Marco Timpanella, Gábor P. Nagy |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Algebraic properties
Physics Automorphism group pure gap Minimum distance 020206 networking & telecommunications 02 engineering and technology Library and Information Sciences Omega Hermitian matrix Computer Science Applications Combinatorics AG-code Weierstrass gap Hermitian curve 0202 electrical engineering electronic engineering information engineering Information Systems |
| Zdroj: | IEEE Transactions on Information Theory. 66:3547-3554 |
| ISSN: | 1557-9654 0018-9448 |
| Popis: | Hermitian functional and differential codes are AG-codes defined on a Hermitian curve. To ensure good performance, the divisors defining such AG-codes have to be carefully chosen, exploiting the rich combinatorial and algebraic properties of the Hermitian curves. In this paper, the case of differential codes $C_{\Omega }(\mathtt {D},m\mathtt {T})$ on the Hermitian curve $\mathscr {H}_{q^{3}}$ defined over $\mathbb {F}_{q^{6}}$ is worked out where $\mathop {\mathrm {supp}}\nolimits (\mathtt {T}):= \mathscr {H}_{q^{3}}(\mathbb {F}_{q^{2}})$ , the set of all $\mathbb {F}_{q^{2}}$ -rational points of $\mathscr {H}_{q^{3}}$ , while $\mathtt {D}$ is taken, as usual, to be the sum of the points in the complementary set $D = \mathscr {H}_{q^{3}}(\mathbb {F}_{q^{6}})\setminus \mathscr {H} _{q^{3}}(\mathbb {F}_{q^{2}})$ . For certain values of $m$ , such codes $C_{\Omega }(\mathtt {D},m\mathtt {T})$ have better minimum distance compared with true values of 1-point Hermitian codes. The automorphism group of $C_{L}(\mathtt {D},m\mathtt {T})$ , $m\leq q^{3}-2$ , is isomorphic to $PGU(3,q)$ . |
| Databáze: | OpenAIRE |
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