On threshold decoding of cyclic codes

Bose-Chaudhuri-Hocquenghem (BCH) codes are very powerful random error-correcting techniques. We have investigated whether all BCH codes can be L-step orthogonalized, and have found a specific class of double error-correcting BCH codes which cannot be L-step orthogonalized. We show further that all BCH codes with length qm − 1, where q is a power of any prime p(q = p8), and all Euclidean geometry codes, can be one-step decoded by parity checks to correct a significant number of errors. These parity vectors need not be orthogonal to each other. For the general case, we have not been able to determine whether they can or cannot be decoded to their minimum distances by such a technique. The above codes decoded by nonorthogonal parity checks in the manner given herein are comparable to projective geometry codes, decoded by Rudolph's method