An alternative to the Hamming code in the class of SEC-DED codes in semiconductor memory

The Pi code constructed by V.I. Panchenko (1987) is studied. The Pi code as an alternative to the Hamming code in the class of single-error-correcting and double-error-detecting codes (SEC-DED codes) is also considered. The Pi code has a smaller number of words of weight 4 and provides a larger probability of triple-independent-error detection than the shortened Hamming code with the same parameters. Shortening algorithms for the Pi code are proposed, and parity check matrices of the (39,32), (72,64), (137,128) shortened Pi codes are constructed. The obtained codes can detect byte errors of length 4. The parity check matrices of the Pi code have more 1´s in rows than corresponding matrices of the Hamming code. The Pi code is a reasonable alternative to the Hamming code in the class of SEC-DED codes.