Abstract:A trilinear alternating form on dimension $n$ can be defined based on a~ Steiner triple system of order $n$. We prove some basic properties of these forms and using the radical polynomial we show that for dimensions up to $15$ nonisomorphic Steiner triple systems provide nonequivalent forms over $GF(2)$. Finally, we prove that Steiner triple systems of order $n$ with different number of subsystems of order $(n-1)/2$ yield nonequivalent forms over $GF(2)$.
Keywords: trilinear alternating form; Steiner triple system; radical polynomial
DOI: DOI 10.14712/1213-7243.2015.182
AMS Subject Classification: 15A69