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List Decoding for Binary Goppa Codes

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Coding and Cryptology (IWCC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6639))

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Abstract

This paper presents a Patterson-style list-decoding algorithm for classical irreducible binary Goppa codes. The algorithm corrects, in polynomial time, approximately \(n-\sqrt{n(n-2t-2)}\) errors in a length-n classical irreducible degree-t binary Goppa code. Compared to the best previous polynomial-time list-decoding algorithms for the same codes, the new algorithm corrects approximately \(t^2\!/2n\) extra errors.

Permanent ID of this document: 210ecf064c479a278ab2c98c379f72e0. Date of this document: 2011.03.02. This work was carried out while the author was visiting Technische Universiteit Eindhoven. This work has been supported in part by the National Science Foundation under grant ITR–0716498 and in part by the Cisco University Research Program.

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Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Chicago, Chicago, IL, 60607–7045, USA

    Daniel J. Bernstein

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  1. Daniel J. Bernstein
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Editor information

Editors and Affiliations

  1. School of Physical and Mathematical Sciences, Division of Mathematical Sciences, Nanyang Technological University, 637371, Singapore

    Yeow Meng Chee , San Ling , Huaxiong Wang  & Chaoping Xing , ,  & 

  2. College of Information Engineering, Qingdao University, 266071, Shandong, P.R. China

    Zhenbo Guo

  3. Qingdao University, 266071, Shandong, P.R. China

    Fengjing Shao

  4. School of Mathematical Sciences, Yangzhou University, 225002, Jiangsu, P.R. China

    Yuansheng Tang

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Bernstein, D.J. (2011). List Decoding for Binary Goppa Codes. In: Chee, Y.M., et al. Coding and Cryptology. IWCC 2011. Lecture Notes in Computer Science, vol 6639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20901-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-20901-7_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20900-0

  • Online ISBN: 978-3-642-20901-7

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