Efficient Forney functions for decoding AG codes - Leonard, D.A. (IEEE transactions on information theory, 1999)
Using a Forney formula to solve for the error magnitudes in decoding algebraic-geometric (AG) codes requires producing functions /spl sigma//sub 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 (see ibid., vol.42, p.1263-8, 1996).