Step-by-step decoding of the Bose-Chaudhuri- Hocquenghem codes

A new and conceptually simple decoding procedure is developed for all of the cyclic Bose-Chaudhuri-Hocquenghem codes. If
t
is the number of errors guaranteed correctable by the Bose-Chaudhuri 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
t \times t
matrix is singular. In the general case, the method requires only the determination of whether a
t \times t
matrix 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.