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Simplified understanding and efficient decoding of a class of algebraic-geometric codes

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4 Author(s)
Gui-Liang Feng ; Center for Adv. Comput. Studies, Southwestern Louisiana Univ., Lafayette, LA, USA ; Wei, V.K. ; Rao, T.R.N. ; Tzeng, K.K.

An efficient decoding algorithm for algebraic-geometric codes is presented. For codes from a large class of irreducible plane curves, including Hermitian curves, it can correct up to [(d*-1)/2] errors, where d* is the designed minimum distance. With it we also obtain a proof of dmin⩾d* without directly using the Riemann-Roch theorem. The algorithm consists of Gaussian elimination on a specially arranged syndrome matrix, followed by a novel majority voting scheme. A fast implementation incorporating block Hankel matrix techniques is obtained whose worst-case running time is O(mn2), where m is the degree of the curve. Applications of our techniques to decoding other algebraic-geometric codes, to decoding BCH codes to actual minimum distance, and to two-dimensional shift register synthesis are also presented

Published in:

Information Theory, IEEE Transactions on  (Volume:40 ,  Issue: 4 )

Date of Publication:

Jul 1994

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