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.
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Augot, D., Stepanov, M. (2009). A Note on the Generalisation of the Guruswami–Sudan List Decoding Algorithm to Reed–Muller Codes. In: Sala, M., Sakata, S., Mora, T., Traverso, C., Perret, L. (eds) Gröbner Bases, Coding, and Cryptography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93806-4_27
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DOI: https://doi.org/10.1007/978-3-540-93806-4_27
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