Steiner forms

Commentationes mathematicae Universitatis Carolinae

Jan Hora¹ 

关键词: trilinear alternating form;    Steiner triple system;    radical polynomial;   

DOI  :  10.14712/1213-7243.2015.182

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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 $GF(2)$.

【 授权许可】

CC BY