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Maximal Partial Spreads and Flocks

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Abstract

Denote by ℱ a flock of a quadratic cone of PG(3,q) by S(ℱ) the spread of PG(3,q) associated with ℱ and by l∞ the common line of the base reguli. Suppose that there are two lines not transversal to a base regulus which share the same lines of S(ℱ) Then we prove that ℱ is either linear or a Kantor-Knuth semifield flock. Using this property we can extend the result of J3 on derivable flocks proving that, if a set of q + 1 lines of S(ℱ) defines a derivable net different from a base regulus-net, then ℱ is either linear or a Kantor-Knuth semifield flock. Moreover if l∞ is not a component of the derivable net, then ℱ is linear.

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Authors
  1. Norman L. Johnson
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  2. Guglielmo Lunardon
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Johnson, N.L., Lunardon, G. Maximal Partial Spreads and Flocks. Designs, Codes and Cryptography 10, 193–202 (1997). https://doi.org/10.1023/A:1008296404711

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  • DOI: https://doi.org/10.1023/A:1008296404711

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