Abstract
A combinatorial characterization of resolvable Steiner 2-(v, k, 1) designs embeddable as maximal arcs in a projective plane of order \((v-k)/(k-1)\) is proved, and a generalization of a conjecture by Andries Brouwer (Geometries and groups, Springer, Heidelberg, 1981) is formulated.
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Acknowledgments
The author wish to thank the anonymous referees for carefully reading the manuscript and suggesting several improvements, including the open question formulated in Remark 2.2. Research was supported by NSA Grant H98230-16-1-0011.
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Dedicated to Andries Brouwer on the occasion of his 65th birthday.
This is one of several papers published in Designs, Codes and Cryptography comprising the special issue in honor of Andries Brouwer’s 65th birthday.
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Tonchev, V.D. On resolvable Steiner 2-designs and maximal arcs in projective planes. Des. Codes Cryptogr. 84, 165–172 (2017). https://doi.org/10.1007/s10623-016-0243-2
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DOI: https://doi.org/10.1007/s10623-016-0243-2