
Code help
Prove that a code is derrorcorrecting if and only if it is (2d)error detecting.
The Fano code is 2 errordetecting, and it is 1errorcorrecting, so i was thinking of using this as the basis step of induction..
assume: d error correcting $\displaystyle \implies$ 2d error detecting
prove: d+1 error correcting $\displaystyle \implies$ 2(d+1) error detecting
d + 1 error correcting $\displaystyle \implies$ 2d error detecting + 2 error detecting. (induction assumption)
= 2(d+1)error detecting.
if this works then.... i can just use the same method to
Prove: that 2d error detecting $\displaystyle \implies$ d error correcting