$3$-designs derived from plane algebraic curves
Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 817-823
Published online December 1, 2007
Hoseog Yu
Sejong University
Abstract : In this paper, we develop a simple method for computing the stabilizer subgroup of a subgroup of $$D(g)=\{\alpha \in \f_q \mid \text{there is a } \beta \in \f_q^{\times} \text{ \ such that \ } \beta^n=g(\alpha) \}$$ in $PSL_2(\f_q)$, where $q$ is a large odd prime power, $n$ is a positive integer dividing $q-1$, and $g(x) \in \f_q[x]$. As an application, we construct new infinite families of $3$-designs (cf. Examples~\ref{ex11} and~\ref{ex22}).
Keywords : $3$-designs, stabilizer group
MSC numbers : Primary 05B05
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