Efficient Forney functions for decoding AG codes

Authors
Citation
Da. Leonard, Efficient Forney functions for decoding AG codes, IEEE INFO T, 45(1), 1999, pp. 260-265
Citations number
21
Categorie Soggetti
Information Tecnology & Communication Systems
Journal title
IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN journal
00189448 → ACNP
Volume
45
Issue
1
Year of publication
1999
Pages
260 - 265
Database
ISI
SICI code
0018-9448(199901)45:1<260:EFFFDA>2.0.ZU;2-I
Abstract
Using a Forney formula to solve for the error magnitudes in decoding AG cod es 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 prod uced 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 u sing the FGLM algorithm. These two steps essentially complete the efficient decoding scheme based on a Forney formula started in the author's previous work.