Weight distribution and performance of the iterated product of single-parity-check codes

We consider the iterated product of single-parity-check (SPC) codes. We show that their weight distribution asymptotically approaches that of random coding if the smallest code length in the product approaches infinity. According to a specific criterion, the best choice consists of taking all SPC codes of equal length. Estimates of the weight distribution obtained by simulation show that even moderately long codes have a weight distribution close to that obtained in the average by random coding. We also discuss decoding of these codes by iterated replication decoding and report results of its simulation.