A Note on the Generalisation of the Guruswami–Sudan List Decoding Algorithm to Reed–Muller Codes

Daniel Augot () and Michael Stepanov ()
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Daniel Augot: Project-Team Secret, INRIA Paris-Rocquencourt
Michael Stepanov: St. Petersburg State University of Aerospace Instrumentation

A chapter in Gröbner Bases, Coding, and Cryptography, 2009, pp 395-398 from Springer

Abstract: 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.

Keywords: Strong Form; Polynomial Identity; Probabilistic Algorithm; Dimensional Array; Austrian Academy (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-93806-4_27

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DOI: 10.1007/978-3-540-93806-4_27

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