Introductory Computer Methods and Numerical Analysis
- R. H. Pennington
- New York: MacMillan,
A new and conceptually simple decoding procedure is developed for all of the cyclic Bose-Chaudhuri-Hocquenghem codes. If f is the number of errors guaranteed correctable by the BoseChaudhuri bound, then any pattern of t 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 f X f matrix is singular. In the general case, the method requires only the determination of whether a f X t matrix and a (f + 1) X (1 + 1) 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.