Abstract
The famous Dembowski-Wagner theorem gives various characterizations of the classical geometric 2-design PGn-1(n, q) among all 2-designs with the same parameters. One of the characterizations requires that all lines have size q + 1. It was conjectured [2] that this is also true for the designs PG d (n, q) with 2 ≤ d ≤ n − 1. We establish this conjecture, hereby improving various previous results.
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Communicated by D. Jungnickel.
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Metsch, K. A generalization of a result of Dembowski and Wagner. Des. Codes Cryptogr. 60, 277–282 (2011). https://doi.org/10.1007/s10623-010-9432-6
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DOI: https://doi.org/10.1007/s10623-010-9432-6