Generalized Reed - Solomon codes from algebraic geometry
JH van Lint, T. A. Springer · IEEE Transactions on Information Theory · 1987
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.