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

@article{Heegard1995SystematicEV,
  title={Systematic encoding via Grobner bases for a class of algebraic-geometric Goppa codes},
  author={Chris Heegard and J. Little and Keith Saints},
  journal={IEEE Trans. Information Theory},
  year={1995},
  volume={41},
  pages={1752-1761}
}
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. Index TermsSystematic encoding, algebraic-geometric Goppa codes, Grobner bases. 

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On the structure of Hermitian codes , ” J . Pure Appl . Algebra , to appear , May 1995 . S . Sakata , “ A GrGbner basis and a minimal polynomial set , of a finite nD array , ”

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