DocumentCode :
907095
Title :
Step-by-step decoding of the Bose-Chaudhuri- Hocquenghem codes
Author :
Massey, James L.
Volume :
11
Issue :
4
fYear :
1965
fDate :
10/1/1965 12:00:00 AM
Firstpage :
580
Lastpage :
585
Abstract :
A new and conceptually simple decoding procedure is developed for all of the cyclic Bose-Chaudhuri-Hocquenghem codes. If 
is the number of errors guaranteed correctable by the Bose-Chaudhuri bound, then any pattern of or fewer errors can be corrected in a step-by-step manner using this procedure. In the binary case, the method requires only the determination of whether a 
matrix is singular. In the general case, the method requires only the determination of whether a matrix and a 
matrix are simultaneously singular. Circuits to implement the algorithm are developed and two detailed examples are given. Finally, the step-by-step procedure is compared to other known methods for decoding the Bose-Chaudhuri-Hocquenghem codes.
is the number of errors guaranteed correctable by the Bose-Chaudhuri bound, then any pattern of or fewer errors can be corrected in a step-by-step manner using this procedure. In the binary case, the method requires only the determination of whether a matrix is singular. In the general case, the method requires only the determination of whether a matrix and a matrix are simultaneously singular. Circuits to implement the algorithm are developed and two detailed examples are given. Finally, the step-by-step procedure is compared to other known methods for decoding the Bose-Chaudhuri-Hocquenghem codes.Keywords :
BCH codes; Decoding; Circuits; Decoding; Error correction; Galois fields; Polynomials; Redundancy; Testing;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1965.1053833
Filename :
1053833
Link To Document :
