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Keywords:
trilinear alternating form; Steiner triple system; radical polynomial
trilinear alternating form; Steiner triple system; radical polynomial
Summary:
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 $GF(2)$.
References:
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