Capability of the error-trapping technique in decoding cyclic codes
Anader Benyamin-Seeyar, S. Shiva, V.K. Bhargava · IEEE Transactions on Information Theory · 1986
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}).