Approximately Gaussian weight distribution of the iterated product of single-parity-check codes

It has been argued by Battail (see Ann. Telecommun., vol. 44, no. 7/8, p. 392-404, 1989) that for the goodness of long block codes a better criterion to use than the minimum Hamming distance is the closeness of the normalised weight distribution of the code to a Gaussian distribution. Certain iterated-product codes have recently been shown to provide good performance in spite of having a relatively poor Hamming distance. The authors substantiate the arguments of Battail by showing that these iterated-product codes have a weight distribution that is approximately Gaussian even for relatively short lengths