We present a new way to find all possible error patterns up to a given weight greater than the designed error correcting capability (e/sub BCH/). Possible error positions are localized by indicators. Our method can be seen as an extension of the step-by-step decoder introduced by Massey (1965) for BCH codes. We consider the decoding of binary cyclic codes.

The Zetterberg codes are one of the best known families of double-error correcting binary linear codes. Unfortunately, no satisfactory decoding algorithm has been known for them until recently when an algebraic decoding algorithm was described by P. Kallquist (1989). It requires, however, to solve a quadratic equation in order to decide whether 2 or 3 errors have occurred. A simple criterion is derived to determine whether 1, 2, or 3 errors have occurred when a Zetterberg code is used for data transmission. Based on criterion a new decoding algorithm is proposed which is faster than the known one.>