Geodesic
New infinite families of 3-designs from algebraic curves of higher genus over finite fields
The electronic journal of combinatorics, Tome 14 (2007)
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In this paper, we give a simple method for computing the stabilizer subgroup of $D(f)=\{\alpha \in {\Bbb F}_q \mid \text{ there is a } \beta \in {\Bbb F}_q^{\times} \text{ such that }\beta^n=f(\alpha)\}$ in $PSL_2({\Bbb F}_q)$, where $q$ is a large odd prime power, $n$ is a positive integer dividing $q-1$ greater than $1$, and $f(x) \in {\Bbb F}_q[x]$. As an application, we construct new infinite families of $3$-designs.
DOI : 10.37236/1026
Classification : 05B05 
@article{10_37236_1026,
     author = {Byeong-Kweon Oh and Hoseog Yu},
     title = {New infinite families of 3-designs from algebraic curves of higher genus over finite fields},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/1026},
     zbl = {1157.05306},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1026/}
}
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Byeong-Kweon Oh; Hoseog Yu. New infinite families of 3-designs from algebraic curves of higher genus over finite fields. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/1026

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