# distance of a code name in scheme

i wonder: is it true that if we take a information word, call it M(with m bits) for example, and code it by first coding M using a code, that we don't know anything about, except of it a length of k, when k>2, and after that we add to the obtained word an even(not odd) bit.

if we know that k is even, does it mean that the length of the code is k+1? does it even matter if k is even or odd?

what i think:

if the code is a code with length k, when k>2, then it should be able to fix $$\lfloor \frac{k-1}{2}\:\rfloor$$ (if possible, i would really appreciate elaboration on this to really understand it deeper). i don't think that the length of the code is necessarily k+1, because if the code is even bit, then in the second step we'll always get addition of 0, but the distance is still 2.

i am not sure though what would've happened if k was odd(not even).