Riemann–Roch spaces of the Hermitian function field with applications to algebraic geometry codes and low-discrepancy sequences

This paper is concerned with two applications of bases of Riemann–Roch spaces. In the first application, we define the floor of a divisor and obtain improved bounds on the parameters of algebraic geometry codes. These bounds apply to a larger class of codes than that of Homma and Kim (J. Pure Appl. Algebra 162 (2001) 273). Then we determine explicit bases for large classes of Riemann–Roch spaces of the Hermitian function field. These bases give better estimates on the parameters of a large class of m-point Hermitian codes. In the second application, these bases are used for fast implementation of Xing and Niederreiterʹs method (Acta. Arith. 72 (1995) 281) for the construction of low-discrepancy sequences.