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Achieving the designed error capacity in decoding algebraic-geometric codes

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1 Author(s)
Ehrhard, D. ; Math. Inst. IV, Heinrich-Heine-Univ., Dusseldorf, Germany

A decoding algorithm for codes arising from algebraic curves explicitly constructable by Goppa's construction is presented. Any configuration up to the greatest integer less than or equal to (d *-1)/2 errors is corrected by the algorithm whenever d*⩾6g, where d* is the designed minimum distance of the code and g is the genus of the curve. The algorithm's complexity is at most O((d*)2 n), where n denotes the length of the code. Application to Hermitian codes and connections with well-known algorithms are explained

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Information Theory, IEEE Transactions on  (Volume:39 ,  Issue: 3 )