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On sets of points with few odd secants

  • Simeon Ball (a1) and Bence Csajbók (a2)

Abstract

We prove that, for q odd, a set of q + 2 points in the projective plane over the field with q elements has at least 2qc odd secants, where c is a constant and an odd secant is a line incident with an odd number of points of the set.

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Corresponding author

*Corresponding author. Email: simeon@ma4.upc.edu

Footnotes

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The first author acknowledges the support of project MTM2017-82166-P of the Spanish Ministerio de Economía y Competitividad.

The second author is supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. The second author acknowledges the support of OTKA grant K 124950.

Footnotes

References

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[9] Csajbók, B. (2018) On bisecants of Rédei type blocking sets and applications. Combinatorica 38 143166.
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[12] Szönyi, T. and Weiner, Z. (2014) On the stability of the sets of even type. Adv. Math. 267 381394.
[13] Vandendriessche, P. (2015) On small line sets with few odd-points. Des. Codes Cryptogr. 75 453463.

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On sets of points with few odd secants

  • Simeon Ball (a1) and Bence Csajbók (a2)

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