Efficient Forney functions for decoding AG codes
Using a Forney formula to solve for the error magnitudes in decoding AG codes requires producing functions sigma(P), which are 0 at all but one point P of the variety of the error-locator ideal. The best such function is produced here in a reasonably efficient way from a lex Grobner basis. This lex basis is, in turn, produced efficiently from a weighted, grevlex basis by using the FGLM algorithm. These two steps essentially complete the efficient decoding scheme based on a Forney formula started in the author's previous work.
forney formula fglm algorithm algebraic-geometric (ag) codes grobner bases