I have to prove that the repetition code is the only linear code with parameters $[n,1,n]$, up to equivalence of codes.
In order to show this, is it enough to say that equivalent codes have the same parameters (I already proved this), thus any $[n,1,n]$ code is equivalent to the repetition code, and therefore the repetition code is the only linear code with parameters $[n,1,n]$, up to equivalence of codes?
This seems like a rather silly question to ask on a homework assignment, do you think I'm supposed to first prove that the repetition code has indeed these parameters?