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Any linear code with a nontrivial automorphism has the structure of a module over a polynomial ring. The theory of Griihner bases for modules gives a compact description and implementation of a systematic encoder. We present examples of algebraic-geometric Goppa codes that can be encoded by these methods, including the one-point Hermitian codes. L ET X be a… (More)

In this paper, it is proved that any algehraic-geometric code can be expressed as a cross section of an extended multidimensional cyclic code. Both algebraic-geometric codes and multidimensional cyclic codes are described by a unified theory of linear block codes defined over point sets: algebraic-geometric codes are defined over the points of an algebraic… (More)

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