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*>or=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*)/sup 2/n), where n denotes the length of the code. Application to Hermitian codes and connections with well-known algorithms are explained.>