# A NOTE ON NULL DESIGNS OF DUAL POLAR SPACES

CHO, SOO-JIN

• Published : 2005.01.01
• 54 8

#### Abstract

Null designs on the poset of dual polar spaces are considered. A poset of dual polar spaces is the set of isotropic subspaces of a finite vector space equipped with a nondegenerate bilinear form, ordered by inclusion. We show that the minimum number of isotropic subspaces to construct a nonzero null t-design is ${\prod}^{t}_{i=0}(1+q^{i})$ for the types $B_N,\;D_N$, whereas for the case of type $C_N$, more isotropic subspaces are needed.

#### Keywords

null designs;minimal null designs;dual polar spaces

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