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Generalized Reed - Solomon codes from algebraic geometry

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2 Author(s)

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.

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Information Theory, IEEE Transactions on  (Volume:33 ,  Issue: 3 )