  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.
