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The New Minimum Distance Bounds of Goppa Codes and Their Decoding

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Abstract

A couple of new lower bounds of the minimum distance of Goppa codes is derived, using an extended field code for a Goppa code which contains the Goppa code as its subfield-subcode. Also presented are procedures for both error-only and error-and-erasure decoding for Goppa codes up to the new lower bounds, based on the Berlekamp-Massey algorithm and the Feng-Tzeng multisequence shift-register synthesis algorithms which have been used for decoding cyclic codes up to the BCH and HT(Hartmann-Tzeng) bounds.

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Authors and Affiliations

  1. Department of Computer Science, Dankook University, Anseo-Dong, Chonan, Choongnam, Korea, 330–714

    Chang-Seop Park

  2. Center for Advanced Computer Studies, University of Southern Louisiana, Lafayette, LA, 70504

    Gui-Liang Feng

  3. Department of Computer Science and Electrical Engineering, Lehigh University, Bethlehem, PA, 18015

    Kenneth K. Tzeng

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  1. Chang-Seop Park
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  2. Gui-Liang Feng
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  3. Kenneth K. Tzeng
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Park, CS., Feng, GL. & Tzeng, K.K. The New Minimum Distance Bounds of Goppa Codes and Their Decoding. Designs, Codes and Cryptography 9, 157–176 (1996). https://doi.org/10.1023/A:1018066030299

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