Generalized Reed-Solomon codes from algebraic geometry

Authors:
J. H. van Lint;T. A. Springer
Affiliations:
Eindhoven Univ. of Technology, Eindhoven, The Netherlands;Univ. of Utrecht, Utrecht, The Netherlands
Venue:
IEEE Transactions on Information Theory
Year:
1987

Citing 0
Cited 4

Jack van Lint (1932-2004): a survey of his scientific work

Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
Coding for a multiple access OR channel: A survey

Discrete Applied Mathematics
Nonbinary quantum codes from hermitian curves

AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

Cryptography and Communications

Quantified Score

Hi-index	754.85

Visualization

Abstract

A few years ago Tsfasman {em et al.,} using results from algebraic geometry, showed that there is a sequence of codes which are generalizations of Goppa codes and which exceed the Gilbert-Varshamov bound. We show that a similar sequence of codes (in fact, the duals of the previous codes) can be found by generalizing the construction of Reed-Solomon codes. Our approach has the advantage that it uses less complicated concepts from algebraic geometry.