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Efficient Forney functions for decoding AG codes

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1 Author(s)
Leonard, D.A. ; Dept. of Discrete & Statistical Sci., Auburn Univ., AL, USA

Using a Forney formula to solve for the error magnitudes in decoding algebraic-geometric (AG) codes requires producing functions σP, 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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Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 1 )