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On Representations of Algebraic-Geometric Codes for List Decoding

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Book cover Algorithms - ESA 2000 (ESA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1879))

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Abstract

We show that all algebraic-geometric codes possess a succinct representation that allows for the list decoding algorithms of [15, 7] to run in polynomial time. We do this by presenting a root-finding algorithm for univariate polynomials over function fields when their coefficients lie in finite-dimensional linear spaces, and proving that there is a polynomial size representation given which the root finding algorithm runs in polynomial time.

Supported in part by an MIT-NEC Research Initiation Award, a Sloan Foundation Fellowship and NSF Career Award CCR-9875511.

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Author information

Authors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139

    Venkatesan Guruswami & Madhu Sudan

Authors
  1. Venkatesan Guruswami
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  2. Madhu Sudan
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK

    Mike S. Paterson

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Guruswami, V., Sudan, M. (2000). On Representations of Algebraic-Geometric Codes for List Decoding. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_23

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  • DOI: https://doi.org/10.1007/3-540-45253-2_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41004-1

  • Online ISBN: 978-3-540-45253-9

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