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...
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| Veröffentlicht in: | IEEE transactions on information theory Jg. 45; H. 1; S. 260 - 265 |
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| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
IEEE
01.01.1999
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Schlagworte: | |
| ISSN: | 0018-9448, 1557-9654 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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). |
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| Bibliographie: | 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 |