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On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes

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Book cover Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2227))

Abstract

Fast interpolation methods for the original and improved versions of list decoding of one-point algebraic-geometry codes are presented. The methods are based on the Gröbner basis theory and the BMS algorithm for multiple arrays, although their forms are different in the original list decoding algorithm (Sudan algorithm) and the improved list decoding algorithm (Guruswami-Sudan algorithm). The computational complexity is less than that of the conventional Gaussian elimination method.

This work is partly supported by the Science Foundation of the Japanese Educational Ministry under Grant No. 12650368.

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Author information

Authors and Affiliations

  1. Department of Information and Communication Engineering, The University of Electro-Communications, 1-5-1 Chofugaoka Chofu-shi, 182-8585, Tokyo, Japan

    Shojiro Sakata

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  1. Shojiro Sakata
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Editor information

Editors and Affiliations

  1. Department of Mathematics, RMIT University, GPO Box 2476V, 3001, Melbourne, Australia

    Serdar Boztaş

  2. Department of Computing, Macquarie University, 2109, NSW, Australia

    Igor E. Shparlinski

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© 2001 Springer-Verlag Berlin Heidelberg

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Sakata, S. (2001). On Fast Interpolation Method for Guruswami-Sudan List Decoding of One-Point Algebraic-Geometry Codes. In: Boztaş, S., Shparlinski, I.E. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2001. Lecture Notes in Computer Science, vol 2227. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45624-4_18

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  • DOI: https://doi.org/10.1007/3-540-45624-4_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42911-1

  • Online ISBN: 978-3-540-45624-7

  • eBook Packages: Springer Book Archive

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