I've been reading about upper bounds for codes, and I'm currently looking at constant weight codewords.
A $(n, M, d)$ code $\mathcal{C}$ over $\mathbb{F}_q$ is a constant weight code provided every codeword was the same weight $w$. Furthermore, $A_q(n, d, w)$ denotes the maximum number of codewords in a constant weight $(n, M)$ code over $\mathbb{F}_q$ of length $n$ and minimum distance at least $d$ whose codewords have weight $w$. Then, the text introduces the Restricted Johnson Bound for $A_q(n, d, w)$ and proves it.
From here, there are several problems in the text. One problem in particular deals with $A_2(10, 6, 4)$. By using the Restricted Johnson Bound, I am able to show that $A_2(10, 6, 4) \leq 5$. To show that $A_2(10, 6, 4) = 5$, I have to construct a $(10, 5, 6)$ constant weight binary code with codewords of weight $4$.
I am having trouble with this construction and was wondering if anyone could help me out. Any help would be greatly appreciated!