Systematic encoding via Grobner bases for a class of algebraic-geometric Goppa codes

Authors:
C. Heegard;J. Little;K. Saints
Affiliations:
Sch. of Electr. Eng., Cornell Univ., Ithaca, NY;-;-
Venue:
IEEE Transactions on Information Theory - Part 1
Year:
2006

Citing 0
Cited 3

Cited References

Computer algebra handbook
Low complexity encoder for generalized quasi-cyclic codes coming from finite geometries

ICC'09 Proceedings of the 2009 IEEE international conference on Communications
Gröbner basis for norm-trace codes

Journal of Symbolic Computation

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Abstract

Any linear code with a nontrivial automorphism has the structure of a module over a polynomial ring. The theory of Grobner 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