Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Weierstrass Pairs and Minimum Distance of Goppa Codes
Designs, Codes and Cryptography
On Goppa Codes and Weierstrass Gaps at Several Points
Designs, Codes and Cryptography
Geometric Reed-Solomon codes of length 64 and 65 over F8
IEEE Transactions on Information Theory
Low-Discrepancy Sequences and Global Function Fields with Many Rational Places
Finite Fields and Their Applications
Weierstrass Semigroups and Codes from a Quotient of the Hermitian Curve
Designs, Codes and Cryptography
Minimum distance decoding of general algebraic geometry codes via lists
IEEE Transactions on Information Theory
On the floor and the ceiling of a divisor
Finite Fields and Their Applications
The order bound for general algebraic geometric codes
Finite Fields and Their Applications
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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 Niederreiter's method (Acta. Arith. 72 (1995) 281) for the construction of low-discrepancy sequences.