I am interested in the maximal number of $k$-subsets of an $n$-set such that any two subsets meet in at most $(k-2)$ points. I found that for $k=3$ and $k=4$, we have the sequences http://oeis.org/A001839 and http://oeis.org/A001843 as solutions which gives the impression that higher orders should be obtainable via $A(n,4,k)$ but this seems to be complicated when I look at the research invested in $A$. 


"A binary constant weight code of word length $n$ and weight $w$ and minimum
distance $d$ is a collection of $(0,1)$-vectors of length $n$, all having $w$ ones and
$n\cdot w$ zeros, such that any two of these vectors differ in at least $d$ places. The
maximum size of such a code is denoted by $A(n; d;w)$."
The definition of $A$ can be found here https://www.win.tue.nl/~aeb/preprints/cw4p.pdf.     

I tried to say something about cases $k>5$ using the [Erdös-Ko-Rado Theorem][1] but I was not really succesfull. Is my intuition right, that $A(n,4,k)$ described exactly the quantity, which I am looking for? 


  [1]: https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Ko%E2%80%93Rado_theorem