A new family of tight sets in Q(+)(5, q)

作者：De Beule Jan; Demeyer Jeroen; Metsch Klaus; Rodgers Morgan^*

来源：Designs, Codes and Cryptography, 2016, 78(3): 655-678.

DOI：10.1007/s10623-014-0023-9

• Tight sets
• Cameron-Liebler line classes
• Sets of type (m, n)
• Tactical decompositions

In this paper, we describe a new infinite family of -tight sets in the hyperbolic quadrics , for . Under the Klein correspondence, these correspond to Cameron-Liebler line classes of having parameter . This is the second known infinite family of nontrivial Cameron-Liebler line classes, the first family having been described by Bruen and Drudge with parameter in for all odd . The study of Cameron-Liebler line classes is closely related to the study of symmetric tactical decompositions of (those having the same number of point classes as line classes). We show that our new examples occur as line classes in such a tactical decomposition when (so for some positive integer ), providing an infinite family of counterexamples to a conjecture made by Cameron and Liebler (in Linear Algebra Appl 46, 91-102, 1982); the nature of these decompositions allows us to also prove the existence of a set of type in the affine plane for all positive integers . This proves a conjecture made by Rodgers in his Ph.D. thesis.

• 出版日期2016-3