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A note on null designs of dual polar spaces

Soojin Cho
대한수학회 (The Korean Mathematical Society)|2005.01|대한수학회논문집 (Communications of the KMS)|제20권 제1호|pp. 15-21

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Abstract

Null designs on the poset of dual polar spaces are con-sidered. A poset of dual polar spaces is the set of isotropic sub-spaces of a ¯nite vector space equipped with a nondegenerate bilin-ear form, ordered by inclusion. We show that the minimum num-ber of isotropic subspaces to construct a nonzero null t-design is Qti=0(1 + qi) for the types BN, DN, whereas for the case of type CN, more isotropic subspaces are needed.

참고문헌 (9)

  1. "Simple groups of Lie type" (1972)
  2. "Minimal null designs and a density theorem of posets", 19, pp.433~440 (1998)
  3. "Minimal null designs of subspace lattice over nite elds", 282, pp.199~220 (1998)
  4. "On the support size of null designs of nite ranked posets", 19, pp.589~595 (1999)
  5. "On the number of sets in a nullt-design", 4, pp.21~23 (1983)
  6. "Representations of general linear groups" (1984), Cambridge University Press
  7. "Combinatorial Sn -modules as codes", 4, pp.47~68 (1995)
  8. "Some q-Krawtchouk polynomials on Chevalley groups", 102, pp.625~662 (1986)
  9. "t-designs in classical association schemes", 2, pp.283~286 (1980)

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