A note on the generalisation of the Guruswami-Sudan list decoding algorithm to reed-muller codes

Abstract

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. © 2009 Springer-Verlag Berlin Heidelberg.