Showing papers on "Goppa code published in 1977"
TL;DR: 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) codesCan be decoded using O-log n arithmetic Operations, and iii) Justesen's asymptotically good codes can been decoded use O( n^{2}) bit operations.
Abstract: 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.
36 citations
TL;DR: It is shown how the theory of continued fractions for polynomials can be used for the decoding of a class of codes which contains Goppa codes.
Abstract: It is shown how the theory of continued fractions for polynomials can be used for the decoding of a class of codes which contains Goppa codes.
17 citations