2009 | OriginalPaper | Buchkapitel
A Note on the Generalisation of the Guruswami–Sudan List Decoding Algorithm to Reed–Muller Codes
verfasst von : Daniel Augot, Michael Stepanov
Erschienen in: Gröbner Bases, Coding, and Cryptography
Verlag: Springer Berlin Heidelberg
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We revisit the generalisation of the Guruswami–Sudan list decoding algorithm to Reed–Muller codes. Although the generalisation is straightforward, the analysis is more difficult than in the Reed–Solomon case. A previous analysis has been done by Pellikaan and Wu (List decoding of
q
-ary Reed–Muller codes, Tech. report, from the authors,
2004a
; IEEE Trans. on Inf. Th. 50(4): 679–682,
2004b
), relying on the theory of Gröbner bases We give a stronger form of the well-known Schwartz–Zippel Lemma (Schwartz in J. Assoc. Comput. Mach. 27(4): 701–717,
1980
; Zippel in Proc. of EUROSAM 1979, LNCS, vol. 72, Springer, Berlin, pp. 216–226,
1979
), taking multiplicities into account. Using this Lemma, we get an improved decoding radius.