A non‐existence result on Cameron–Liebler line classes |
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Authors: | J De Beule A Hallez L Storme |
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Institution: | Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281‐S22, 9000 Ghent, Belgium |
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Abstract: | Cameron–Liebler line classes are sets of lines in PG(3, q) that contain a fixed number x of lines of every spread. Cameron and Liebler classified Cameron–Liebler line classes for x ∈ {0, 1, 2, q2 ? 1, q2, q2 + 1} and conjectured that no others exist. This conjecture was disproven by Drudge for q = 3 8] and his counterexample was generalized to a counterexample for any odd q by Bruen and Drudge 4]. A counterexample for q even was found by Govaerts and Penttila 9]. Non‐existence results on Cameron–Liebler line classes were found for different values of x. In this article, we improve the non‐existence results on Cameron–Liebler line classes of Govaerts and Storme 11], for q not a prime. We prove the non‐existence of Cameron–Liebler line classes for 3 ≤ x < q/2. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 342–349, 2008 |
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Keywords: | Cameron– Liebler line classes blocking sets minihypers spreads tight sets |
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