Hi

I would really appreciate some help in proving the so called plotkin bound

$\displaystyle d\leq \frac{2^{k-1}\cdot n}{2^{k}-1}$

holds for C where C is a binary (n,k,d)-code.

I have been asked to show this by arguing as follows:

For a given position j, show that the number of codewords that have 0 at position j is either $\displaystyle 2^{k}$ or $\displaystyle 2^{k-1}$

I have done this by induction but its a realllyyy long proof so I am looking for a better one if it exists!

Thanks