An experimental study of a binary code

Elias has described a coding system which consists essentially of iterating the Hamming code1 and has obtained estimates of the probability of error after each iteration on the assumption that each set of check bits is used once and then discarded. It seemed that the first set of check bits could be reused profitably after some errors were corrected with the second set of check bits but the analysis is seriously complicated by the interdependence of errors. Therefore an experimental study of codes of this type was made using the IBM 704. Matrices of 8 by 16, 16 by 32, and 32 by 64 bits with Hamming single-error correcting, double-error detecting codes in each column and each row, were used. Errors were introduced randomly, and the Hamming correction procedure was then applied alternately to rows and columns. The results of the experiment and some properties of the code pertinent to their discussion are described in this paper.