Codes and Gap Sequences of Hermitian Curves
Gábor Korchmáros, Gábor P. Nagy, Marco Timpanella · IEEE Transactions on Information Theory · 2019
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 CΩ(D, mT) on the Hermitian curve ℋq3 defined over Fq6 is worked out where su.yppp(T) := ℋq3(Fq2), the set of all Fq2-rational points of ℋq3, while D is taken, as usual, to be the sum of the points in the complementary set D = ℋq3(Fq6) \ℋq3(Fq2). For certain values of m, such codes CΩ(D, mT) have better minimum distance compared with true values of 1-point Hermitian codes. The automorphism group of CL(D, mT), m ≤ q3- 2, is isomorphic to P GU(3, q).