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Decoding Hermitian Codes with Sudan’s Algorithm

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Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1719))

Abstract

We present an efficient implementation of Sudan’s algorithm for list decoding Hermitian codes beyond half the minimum distance. The main ingredients are an explicit method to calculate so-called increasing zero bases, an efficient interpolation algorithm for finding the Q-polynomial, and a reduction of the problem of factoring the Q-polynomial

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References

  1. Madhu Sudan: “Decoding of Reed Solomon Codes beyond the Error-Correction Bound” Journal of Complexity 13, 180–193, 1997.

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  2. M.A. Shokrollahi and H. Wassermann: “List Decoding of Algebraic-Geometric Codes” IEEE Trans. Inform. Theory, vol 45, pp. 432–437, March 1999.

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  3. Venkatesan Guruswami and Madhu Sudan: “Improved Decoding of Reed-Solomon and Algebraic-Geometric Codes” Proc. 39th IEEE Symp. Foundations Comput. Sci., 1998.

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  5. Henning Stichtenoth: “Algebraic function fields and codes” Springer-Verlag,1993.

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  6. Weishi Feng and R. E. Blahut: “Some Results on the Sudan Algorithm”, Proceedings 1998 IEEE International Symposium on Information Theory, p.57, august 1998.

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  7. Ralf Kötter: “On Algebraic Decoding of Algebraic-Geometric and Cyclic Codes” Department of Electrical Engineering, Linköping University, 1996.

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  8. G.-L. Feng and K. K. Tzeng: “A Generalization of the Berlekamp-Massey Algorithm for Multisequence Shift-Register Synthesis with Applications to Decoding Cyclic Codes”,IEEE Trans. Inform. Theory, vol. 37, pp. 1274–1287, Sept. 1991.

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  9. H. Elbr∅nd Jensen, R. Refslund Nielsen, and T. H∅holdt: “Performance analysis of a decoding algorithm for algebraic geometry codes” IEEE Trans. on Inform. Theory, vol.45,pp.1712–1717,July 1999.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technical University of Denmark, Bldg 303, DK-2800, Lyngby, Denmark

    T. Høholdt & R. Refslund Nielsen

Authors
  1. T. Høholdt
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  2. R. Refslund Nielsen
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, University of Hawaii, 2540 Dole St., # 483, Honolulu, HI, 96822, USA

    Marc Fossorier  & Shu Lin  & 

  2. Institute of Industrial Science, University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, 106, Japan

    Hideki Imai

  3. AAECC/IRIT, Université Paul Sabatier, 118, Route de Narbonne, F31067, Toulouse, Cedex, France

    Alain Poli

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© 1999 Springer-Verlag Berlin Heidelberg

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Høholdt, T., Nielsen, R.R. (1999). Decoding Hermitian Codes with Sudan’s Algorithm. In: Fossorier, M., Imai, H., Lin, S., Poli, A. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1999. Lecture Notes in Computer Science, vol 1719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46796-3_26

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  • DOI: https://doi.org/10.1007/3-540-46796-3_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66723-0

  • Online ISBN: 978-3-540-46796-0

  • eBook Packages: Springer Book Archive

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