On Steiner Triple Systems and Perfect Codes

Abstract

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.