DocumentCode :
942600
Title :
A transform approach to Goppa codes
Author :
Loeloeian, Mansour ; Conan, Jean
Volume :
33
Issue :
1
fYear :
1987
fDate :
1/1/1987 12:00:00 AM
Firstpage :
105
Lastpage :
115
Abstract :
Based on a finite Fourier transform of codewords over the finite field GF 
, some basic properties of the class of Goppa codes are presented. A new lower bound on the minimum distance for these codes is derived and applied to a subclass of Goppa codes which is. in fact. equivalent to a subset of punctured reversible cyclic codes. Furthermore. it is shown how the class of Goppa codes can be easily decoded in the context of this transformation by using the Berlekamp-Massey decoding algorithm. Through a slight extension of the procedure, it is also shown how this algorithm may be used m decode alternant codes up to their guaranteed error-correction capability.
, some basic properties of the class of Goppa codes are presented. A new lower bound on the minimum distance for these codes is derived and applied to a subclass of Goppa codes which is. in fact. equivalent to a subset of punctured reversible cyclic codes. Furthermore. it is shown how the class of Goppa codes can be easily decoded in the context of this transformation by using the Berlekamp-Massey decoding algorithm. Through a slight extension of the procedure, it is also shown how this algorithm may be used m decode alternant codes up to their guaranteed error-correction capability.Keywords :
DFT; Discrete Fourier transforms (DFT´s); Goppa coding; Reed-Solomon coding; Decoding; Equations; Error correction; Error correction codes; Fourier transforms; Galois fields; Parity check codes; Polynomials; Reed-Solomon codes; Vehicles;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1987.1057276
Filename :
1057276
Link To Document :
