Error-trapping decoding techniques are attractive due to their simple structure. Since 1962 several improved error-trapping methods have been devised in an effort to extend the capability and effectiveness in decoding multiple-error-correcting cyclic codes. Prange (1962) and MacWilliams (1964) introduced a (T, U) permutation group applied to this error-trapping decoding strategy by making use of a set of code-preserving permutation to obtain k error-free positions from which the rest of the code word could be reconstructed. Recently, exact lower bounds on the code length n for (n, k, 2t+1) cyclic codes have been found by using 5-step and 3-step (T, U) permutation groups. The present paper presents a study on the relationship between the code parameters n, k, t and the number of permutation steps s, with t being odd. Some examples on the capability of (T, U) permutation decodable (PD) cyclic codes are illustrated.>

The exact lower bounds on codelength n for three-step (T, U) permutation decodable binary cyclic codes of even-valued error number t (t>or=4) are presented. Since the derivation of these results involves only the error position, the results are applicable to cyclic codes over GF(2/sup m/).>

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 lengthn, for givenk, of the "multiple-error-correcting'' binary(n, k, t)cyclic codes by applying cyclic(T)and squaring(U)(or square rooting) group(T, U)permutations for1)two-step(T, U)permutation decodable codes(todd- and even-valued) and2)three-step(T,U)permutation decodable codes(todd-valued andt = 2). Finally, some general results are presented for the codes that are not permutation decodable for the specific(T, U)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(2^{m}).