Step-by-step decoding of the Bose-Chaudhuri- Hocquenghem codes
J. Massey · IEEE Transactions on Information Theory · 1965
A new and conceptually simple decoding procedure is developed for all of the cyclic Bose-Chaudhuri-Hocquenghem codes. Iftis the number of errors guaranteed correctable by the Bose-Chaudhuri bound, then any pattern oftor 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 at \times tmatrix is singular. In the general case, the method requires only the determination of whether at \times tmatrix and a(t+1) \times (t+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.