On Steiner Triple Systems and Perfect Codes

Using a computer implementation, we show that two more of the Steiner triple systems on \(15\) elements are perfect, i.e., that there are binary perfect codes of length \(15\), generating \(STS\) which have rank \(15\). This answers partially a question posed by Hergert in \({[3]}\).

We also briefly study the inverse problem of generating a perfect code from a Steiner triple system using a greedy algorithm. We obtain codes that were not previously known to be generated by such procedures.