Abstract
For \(n \ge 9\), we construct maximal partial line spreads for non-singular quadrics of \(PG(n,q)\) for every size between approximately \((cn+d)(q^{n-3}+q^{n-5})\log {2q}\) and \(q^{n-2}\), for some small constants \(c\) and \(d\). These results are similar to spectrum results on maximal partial line spreads in finite projective spaces by Heden, and by Gács and Szőnyi. These results also extend spectrum results on maximal partial line spreads in the finite generalized quadrangles \(W_3(q)\) and \(Q(4,q)\) by Pepe, Rößing and Storme.
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The authors thank the referees for their suggestions and remarks which improved the first version of this article.
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This is one of several papers published in Designs, Codes and Cryptography comprising the special topic on “Finite Geometries: A special issue in honor of Frank De Clerck”
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Rottey, S., Storme, L. Maximal partial line spreads of non-singular quadrics. Des. Codes Cryptogr. 72, 33–51 (2014). https://doi.org/10.1007/s10623-012-9788-x
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DOI: https://doi.org/10.1007/s10623-012-9788-x