On the Non-Existence of Certain Cameron-Liebler Line Classes in PG(3, q) View Full Text


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Article Info

DATE

1998-05

AUTHORS

Aiden A. Bruen, Keldon Drudge

ABSTRACT

Our main result is a non-existence theorem for certain families of lines in three dimensional projective space PG(3, q) over a finite field GF(q). Specifically, a Cameron-Liebler line class in PG(3, q) is a set of lines which intersects every spread of PG(3, q) in the same number x of lines (this number is called its parameter). These sets arose in connection with an attempt by Cameron and Liebler to determine the subgroups of PGL(n+1, q) which have the same number of orbits on points (of PG(n, q)) as on lines; they satisfy several equivalent properties. Here we prove that for 2 < x ≤ √q, no Cameron-Liebler line class of parameter x exists in PG(3, q). A relevant general question on incidence matrices is described. More... »

PAGES

127-132

References to SciGraph publications

  • 1991-03. Cameron-Liebler line classes in PG (3,q) in GEOMETRIAE DEDICATA
  • Journal

    TITLE

    Designs, Codes and Cryptography

    ISSUE

    2

    VOLUME

    14

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1008231927955

    DOI

    http://dx.doi.org/10.1023/a:1008231927955

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1050707093


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