Geodesic
A new family of \((q^{4}+1)\)-tight sets with an automorphism group \(F_{4}(q)\)
Tao Feng1 ; Weicong Li2 ; Qing Xiang3
1Zhejiang University
2Great Bay University
3Southern University of Science and Technology
The electronic journal of combinatorics, Tome 32 (2025) no. 2
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In this paper, we construct a new family of $(q^4+1)$-tight sets in $Q(24,q)$ or $Q^-(25,q)$ according as $q=3^f$ or $q\equiv 2\pmod 3$. The novelty of the construction is the use of the action of the exceptional simple group $F_4(q)$ on its minimal module over $F_q$. The proof relies on a more effective way to decide whether a subset of points of a finite classical polar space is an intriguing set or not.
DOI : 10.37236/12879
Classification : 51E20, 05B25, 51A50
Mots-clés : exceptional simple group, intriguing set, polar space, tight set

Tao Feng  1   ; Weicong Li  2   ; Qing Xiang  3

1 Zhejiang University
2 Great Bay University
3 Southern University of Science and Technology 
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     author = {Tao Feng and Weicong Li and Qing Xiang},
     title = {A new family of \((q^{4}+1)\)-tight sets with an automorphism group {\(F_{4}(q)\)}},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {2},
     doi = {10.37236/12879},
     zbl = {1569.51003},
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Tao Feng; Weicong Li; Qing Xiang. A new family of \((q^{4}+1)\)-tight sets with an automorphism group \(F_{4}(q)\). The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/12879

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