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(D, mT) on the Hermitian curve H-q3 defined over F-q6 is worked out where supp(T) := H-q3(F-q2), the set of all F-q2-rational points of H-q3, while D is taken, as usual, to be the sum of the points in the complementary set D = H-q3(F-q6) \ H-q3(F-q2). For certain values of m, such codes C-Omega(D, mT) have better minimum distance compared with true values of 1-point Hermitian codes. The automorphism group of C-L(D, mT), m &lt;= q(3) - 2, is isomorphic to PGU(3, q).

### Codes and Gap Sequences of Hermitian Curves

#### 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(D, mT) on the Hermitian curve H-q3 defined over F-q6 is worked out where supp(T) := H-q3(F-q2), the set of all F-q2-rational points of H-q3, while D is taken, as usual, to be the sum of the points in the complementary set D = H-q3(F-q6) \ H-q3(F-q2). For certain values of m, such codes C-Omega(D, mT) have better minimum distance compared with true values of 1-point Hermitian codes. The automorphism group of C-L(D, mT), m <= q(3) - 2, is isomorphic to PGU(3, q).
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2020
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11391/1547397`
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