Generalized Reed - Solomon codes from algebraic geometry
- 1 May 1987
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 33 (3) , 305-309
- https://doi.org/10.1109/tit.1987.1057320
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.Keywords
This publication has 7 references indexed in Scilit:
- Modular curves and codes with a polynomial constructionIEEE Transactions on Information Theory, 1984
- Codes and informationRussian Mathematical Surveys, 1984
- ALGEBRAICO-GEOMETRIC CODESMathematics of the USSR-Izvestiya, 1983
- Introduction to Coding TheoryPublished by Springer Nature ,1982
- Modular curves, Shimura curves, and Goppa codes, better than Varshamov‐Gilbert boundMathematische Nachrichten, 1982
- Algebraic GeometryPublished by Springer Nature ,1977
- On subfield subcodes of modified Reed-Solomon codes (Corresp.)IEEE Transactions on Information Theory, 1975