Near Maximum-Likelihood Performance of Some New Cyclic Codes Constructed in the Finite-Field Transform Domain

It is shown that some well-known and some new cyclic codes with orthogonal parity-check equations can be constructed in the finite-field transform domain. It is also shown that, for some binary linear cyclic codes, the performance of the iterative decoder can be improved by substituting some of the dual code codewords in the parity-check matrix with other dual code codewords formed from linear combinations. This technique can bring the performance of a code closer to its maximum-likelihood performance, which can be derived from the erroneous decoded codeword whose euclidean distance with the respect to the received block is smaller than that of the correct codeword. For (63,37), (93,47) and (105,53) cyclic codes, the maximum-likelihood performance is realised with this technique.