The feet of orthogonal Buekenhout–Metz unitals

References

[1] N. Abarzúa, R. Pomareda, O. Vega, Feet in orthogonal-Buekenhout-Metz unitals. Adv. Geom. 18 (2018), 229–236. MR3785423 Zbl 1390.5100310.1515/advgeom-2017-0050Search in Google Scholar

[2] A. Aguglia, G. L. Ebert, A combinatorial characterization of classical unitals. Arch. Math. (Basel) 78 (2002), 166–172. MR1888419 Zbl 1006.5100410.1007/s00013-002-8231-3Search in Google Scholar

[3] J. André, Über nicht-Desarguessche Ebenen mit transitiver Translationsgruppe. Math. Z. 60 (1954), 156–186. MR63056 Zbl 0056.3850310.1007/BF01187370Search in Google Scholar

[4] R. D. Baker, G. L. Ebert, Intersection of unitals in the Desarguesian plane. In: Proceedings of the Twentieth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1989), volume 70, 87–94, 1990. MR1041587 Zbl 0695.51009Search in Google Scholar

[5] R. D. Baker, G. L. Ebert, On Buekenhout-Metz unitals of odd order. J. Combin. Theory Ser. A 60 (1992), 67–84. MR1156648 Zbl 0783.0503110.1016/0097-3165(92)90038-VSearch in Google Scholar

[6] S. Barwick, G. Ebert, Unitals in projective planes. Springer 2008. MR2440325 Zbl 1156.51006Search in Google Scholar

[7] W. Bosma, J. Cannon, C. Playoust, The Magma algebra system. I. The user language. J. Symbolic Comput. 24 (1997), 235–265. MR1484478 Zbl 0898.6803910.1006/jsco.1996.0125Search in Google Scholar

[8] R. H. Bruck, R. C. Bose, The construction of translation planes from projective spaces. J. Algebra 1 (1964), 85–102. MR161206 Zbl 0117.3740210.1016/0021-8693(64)90010-9Search in Google Scholar

[9] R. H. Bruck, R. C. Bose, Linear representations of projective planes in projective spaces. J. Algebra 4 (1966), 117–172. MR196590 Zbl 0141.3680110.1016/0021-8693(66)90054-8Search in Google Scholar

[10] F. Buekenhout, Existence of unitals in finite translation planes of order q² with a kernel of order q. Geom. Dedicata 5 (1976), 189–194. MR448236 Zbl 0336.5001410.1007/BF00145956Search in Google Scholar

[11] L. E. Dickson, On families of quadratic forms in a general field. Quart. J. Pure Appl. Math. 39 (1907), 316–333. MR1410619 Zbl 0916.51011Search in Google Scholar

[12] G. L. Ebert, On Buekenhout-Metz unitals of even order. European J. Combin. 13 (1992), 109–117. MR1158804 Zbl 0758.5100610.1016/0195-6698(92)90042-XSearch in Google Scholar

[13] G. L. Ebert, Buekenhout-Tits unitals. J. Algebraic Combin. 6 (1997), 133–140. MR1436531 Zbl 0877.5100810.1023/A:1008691020874Search in Google Scholar

[14] J. Faulkner, G. Van de Voorde, On the equivalence, stabilisers, and feet of Buekenhout-Tits unitals. Des. Codes Cryptogr. 2023. https://doi.org/10.1007/s10623-023-01234-4Search in Google Scholar

[15] J. Faulkner, G. Van de Voorde, On the equivalence, stabilisers, and feet of Buekenhout-Tits unitals. Des. Codes Cryptogr. 2023. https://doi.org/10.1007/s10623-023-01234-410.1007/s10623-023-01234-4Search in Google Scholar

[16] J. W. P. Hirschfeld, T. Szőnyi, Sets in a finite plane with few intersection numbers and a distinguished point. Discrete Math. 97 (1991), 229–242. MR1140805 Zbl 0748.5101110.1016/0012-365X(91)90439-9Search in Google Scholar

[17] M. Lavrauw, T. Popiel, The symmetric representation of lines in PG(𝔽³ ⊗ 𝔽³). Discrete Math. 343 (2020), 111775, 22 pages. MR4045559 Zbl 1433.0506310.1016/j.disc.2019.111775Search in Google Scholar

[18] R. Metz, On a class of unitals. Geom. Dedicata 8 (1979), 125–126. MR533633 Zbl 0403.5100710.1007/BF00147935Search in Google Scholar

[19] B. Segre, Teoria di Galois, fibrazioni proiettive e geometrie non desarguesiane. Ann. Mat. Pura Appl. (4) 64 (1964), 1–76. MR169117 Zbl 0128.1500210.1007/BF02410047Search in Google Scholar

[20] J. A. Thas, A combinatorial characterization of Hermitian curves. J. Algebraic Combin. 1 (1992), 97–102. MR1162643 Zbl 0784.5102310.1023/A:1022437415099Search in Google Scholar