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m-Systems and Partial m-Systemsof Polar Spaces

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Abstract

Let P be a finite classical polar spaceof rank r, with r ≥ 2. A partial m-system M of P, with 0 ≤ m ≤ r - 1,is any set π1,π2,...,πk of k≠ 0 totally singular m-spacesof P such that no maximal totally singular spacecontaining πi has a point in common with (π1∪π2∪... ∪ π_k)-πi, i=1,2,\dots,k. In aprevious paper an upper bound δ for |M|was obtained (Theorem 1). If |M|=δ, then Mis called an m-system of P. For m=0the m-systems are the ovoids of P;for m=r-1 the m-systems are the spreadsof P. In this paper we improve in many cases theupper bound for the number of elements of a partial m-system,thus proving the nonexistence of several classes of m-systems.

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Authors and Affiliations

  1. Department of Mathematics,Cardwell Hall, Kansas State University, Manhattan, Kansas, 66506-2602, U.S.A

    E. E. Shult & J. A. Thas

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  1. E. E. Shult
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  2. J. A. Thas
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Shult, E.E., Thas, J.A. m-Systems and Partial m-Systemsof Polar Spaces. Designs, Codes and Cryptography 8, 229–238 (1996). https://doi.org/10.1023/A:1018053530453

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  • DOI: https://doi.org/10.1023/A:1018053530453

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