On the complexity of decoding Goppa codes (Corresp.)

It is shown that i) erasures-and-errors decoding of Goppa codes can be done using
O(n \log^{2} n)
arithmetic operations, ii) long primitive binary Bose-Chaudhuri-Hocquenghem (BCH) codes can be decoded using
O(n \log n)
arithmetic operations, and iii) Justesen's asymptotically good codes can be decoded using
O(n^{2})
bit operations. These results are based on the application of efficient computational techniques to the decoding algorithms recently discovered by Sugiyama, Kasahara, Hirasawa, and Namekawa.