Generalized Steiner systems with block size three and group size \(g\equiv 3 \pmod 6\). (English) Zbl 0913.05024
Summary: 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 \(g\equiv 3\pmod 6\).
