A New Family of $(q^4+1)$-Tight Sets with an Automorphism Group $F_4(q)
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 effe...
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| Published in | The Electronic journal of combinatorics Vol. 32; no. 2 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
13.05.2025
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| Online Access | Get full text |
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| Summary: | 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. |
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| ISSN: | 1077-8926 1077-8926 |
| DOI: | 10.37236/12879 |