On the complexity of decoding Goppa codes (Corresp.)

D. Sarwate
1977 IEEE Transactions on Information Theory  
It is shown that i) erasures-and-errors decoding of Goppa codes can be done using O(n log2 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(n2) 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.
doi:10.1109/tit.1977.1055732 fatcat:2lvl3z7lfjfgvklvdwc3tchcqu