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

Daniel Augot; Michael Stepanov

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

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

Daniel Augot
, Michael Stepanov

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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.

Original language	English
Title of host publication	Gröbner Bases, Coding, and Cryptography
Publisher	Springer Berlin Heidelberg
Pages	395-398
Number of pages	4
ISBN (Print)	9783540938057
DOIs	https://doi.org/10.1007/978-3-540-93806-4_27
Publication status	Published - 1 Dec 2009
Externally published	Yes

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Cite this

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title = "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 Gr{\"o}bner 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.",

author = "Daniel Augot and Michael Stepanov",

year = "2009",

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doi = "10.1007/978-3-540-93806-4\_27",

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T1 - A note on the generalisation of the Guruswami-Sudan list decoding algorithm to reed-muller codes

AU - Augot, Daniel

AU - Stepanov, Michael

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-540-93806-4_27

DO - 10.1007/978-3-540-93806-4_27

M3 - Chapter

AN - SCOPUS:84872413976

SN - 9783540938057

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EP - 398

BT - Gröbner Bases, Coding, and Cryptography

PB - Springer Berlin Heidelberg

ER -

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

Abstract

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