Geodesic
Steiner forms
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 4, pp. 527-536.

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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 $GF(2)$.
DOI : 10.14712/1213-7243.2015.182
Classification : 15A69
Keywords: trilinear alternating form; Steiner triple system; radical polynomial 
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Hora, Jan. Steiner forms. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 4, pp. 527-536. doi : 10.14712/1213-7243.2015.182. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.182/

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