Abstract
We use the representation \({T_2(\mathcal{O})}\) for Q(4, q) to show that maximal partial ovoids of Q(4, q) of size q 2 − 1, q = p h, p an odd prime, h > 1, do not exist. Although this was known before, we give a slightly alternative proof, also resulting in more combinatorial information of the known examples for q an odd prime.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Finite Geometries”.
This paper is based on joint work with András Gács, started in the autumn of 2008, as a continuation of the work in [4]. His unfortunate and sudden death prevented us from continuing our joint work on the geometrical interpretation of the results. I would like to dedicate this work to András.
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De Beule, J. On large maximal partial ovoids of the parabolic quadric Q(4, q). Des. Codes Cryptogr. 68, 3–10 (2013). https://doi.org/10.1007/s10623-012-9629-y
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DOI: https://doi.org/10.1007/s10623-012-9629-y