About equidistant codes

Question

I am reading a paper called "Digital Signature based on random error-correcting codes". The digital signature propose there is more known as KKS signature. In that paper the authors wrote about equidistant codes. Specifically, if the code has length $n$, dimension $k$ and distance $t$, then $n = \dfrac{q^k-1}{q-1}$ and $t=q^{k-1}$. I would like to known why these results. I am trying to found these results in the famous book McWilliams and Sloane "The theory of error correcting codes" without success. Could you help me plase? Do you known a book with these results?