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Codes and Gap Sequences of Hermitian Curves.
- Source :
-
IEEE Transactions on Information Theory . Jun2020, Vol. 66 Issue 6, p3547-3554. 8p. - Publication Year :
- 2020
-
Abstract
- 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 $PGU(3,q)$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 66
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 143457061
- Full Text :
- https://doi.org/10.1109/TIT.2019.2950207