Efficient Forney functions for decoding AG codes

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 fro...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on information theory Vol. 45; no. 1; pp. 260 - 265
Main Author: Leonard, D.A.
Format: Journal Article
Language:English
Published: New York IEEE 01.01.1999
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Codes
Decoding
Polynomials
Voting
ISSN:0018-9448, 1557-9654
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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).
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
ISSN:0018-9448
1557-9654
DOI:10.1109/18.746805