SC: Secant Spaces and Clifford's Theorem over Finite Fields

Authors:
S. G. Vladuts
Affiliations:
Institut de Mathématiques de Luminy, UPR 9016 du CNRS, Luminy, Case 930, 13288, Marseille cedex 9, Francef1vladut@iml.univ-mrs.frf1
Venue:
Finite Fields and Their Applications
Year:
1998

Citing 5
Cited 0

Geometric approach to higher weights

IEEE Transactions on Information Theory - Part 1
Notes on the asymptotic behavior of the information rate of block codes (Corresp.)

IEEE Transactions on Information Theory
Generalized Hamming weights for linear codes

IEEE Transactions on Information Theory
Generalized Hamming weights of linear codes

IEEE Transactions on Information Theory
The weight hierarchy of higher dimensional Hermitian codes

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present here a combinatorial approach to special divisors and secant divisors on curves over finite fields based on their relations with error-correcting codes. Applying to linear systems on curves over finite fields numerous coding theory bounds one gets a lot of bounds on their dimensions. This approach works for curves with many rational points, which leads, for example, to certain ameliorations of Clifford's theorem for such curves.