Totally self-checking decoders for Hamming SEC codes

It is shown that there exist totally self-checking (TSC) combinational decoders for (n,k) Hamming single error correcting (SEC) codes if and only if n=2/sup r/-1, r=n-k. For shortened (n,k) Hamming SEC codes the modified combinational totally self-checking decoders with minimum testing delay 2/spl les//spl mu/<(n-k) are suggested.