On the capability of (T, U) permutation decoding method

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