Capability of the error-trapping technique in decoding cyclic codes

The error-trapping technique, whenever applicable, is easy to implement. Here we investigate the capability of this technique, specially based on the permutation decoding concept. The object is to give exact lower bounds on the code length , for given , of the "multiple-error-correcting\´\´ binary cyclic codes by applying cyclic and squaring (or square rooting) group permutations for two-step permutation decodable codes odd- and even-valued) and three-step permutation decodable codes odd-valued and . Finally, some general results are presented for the codes that are not permutation decodable for the specific group permutations. The derivation of the results involves only the symbol positions of the errors, and consequently, the results are directly applicable to cyclic codes over GF .