Generalized Steiner Systems With Block Size Three and Group Size Four

Abstract

Generalized Steiner Systems, $\text{GS}(2,3,n,g)$, are equivalent to maximum constant weight codes over an alphabet of size $g+1$ with distance $3$ and weight $3$ in which each codeword has length $n$. We construct Generalized Steiner Triple Systems, $\text{GS}(2,3,n,g)$, when $g=4$.