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The New Minimum Distance Bounds of Goppa Codes and Their Decoding |
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| Authors: | Chang-Seop Park Gui-Liang Feng Kenneth K. Tzeng |
| Affiliation: | (1) Department of Computer Science, Dankook University, Anseo-Dong, Chonan, Choongnam, Korea, 330–714;(2) Center for Advanced Computer Studies, University of Southern Louisiana, Lafayette, LA, 70504;(3) Department of Computer Science and Electrical Engineering, Lehigh University, Bethlehem, PA, 18015 |
| 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. |
| Keywords: | Goppa codes minimum distance BCH bound HT bound |
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