Systematic encoding via Grobner bases for a class of algebraic-geometric Goppa codes
Chris Heegard, John B. Little, Keith Saints · IEEE Transactions on Information Theory · 1995
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.