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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| Vydané v: | IEEE transactions on information theory Ročník 45; číslo 1; s. 260 - 265 |
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| Hlavný autor: | |
| Médium: | Journal Article |
| Jazyk: | English |
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New York
IEEE
01.01.1999
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | 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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| AbstractList | Using a Forney formula to solve for the error magnitudes in decoding algebraic-geometric (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 (see ibid., vol.42, p.1263-8, 1996) Using a Forney formula to solve for the error magnitudes in decoding AG codes requires producing functions sigmap, 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. 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). |
| Author | Leonard, D.A. |
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| Snippet | 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... Using a Forney formula to solve for the error magnitudes in decoding AG codes requires producing functions sigmap, which are 0 at all but one point P of the... Using a Forney formula to solve for the error magnitudes in decoding algebraic-geometric (AG) codes requires producing functions sigma(P), which are 0 at all... |
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| SubjectTerms | Algorithms Codes Decoding Polynomials Voting |
| Title | Efficient Forney functions for decoding AG codes |
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