Generalized Hermitian Codes over GF(2r)

Stanislav Bulygin

In this talk a generalization of Hermitian function field proposed by Garcia and Stichtenoth will be considered. We will look closely at a Weierstrass semigroup of the point at infinity. It turns out that it has more complex structure than its Hermitian counterpart. We will then apply the results on this semigroup in order to investigate dimension of codes constructed on the generalized Hermitian function field over GF(2r). It also turns out that for certain values of the dimension these codes achieve record values of the minimum distance for an alphabet of 8 elements.

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