A finite shift plane can be equivalently defined via abelian relative difference sets as well as planar functions. In this paper, we present a generic way to construct unitals in finite shift planes of odd square order. We investigate various geometric and combinatorial properties of these planes, such as the self-duality, the existence of O’Nan configurations, Wilbrink’s conditions, the designs formed by circles and so on. We also show that our unitals are inequivalent to the unitals derived from unitary polarities in the same shift planes. As designs, our unitals are also not isomorphic to the classical unitals (the Hermitian curves).
Unitals in shift planes of odd order / Trombetti, Rocco; Zhou, Yue. - In: FORUM MATHEMATICUM. - ISSN 1435-5337. - 29:4(2017). [https://doi.org/10.1515/forum-2015-0165]
Unitals in shift planes of odd order
TROMBETTI, ROCCO;ZHOU, YUE
2017
Abstract
A finite shift plane can be equivalently defined via abelian relative difference sets as well as planar functions. In this paper, we present a generic way to construct unitals in finite shift planes of odd square order. We investigate various geometric and combinatorial properties of these planes, such as the self-duality, the existence of O’Nan configurations, Wilbrink’s conditions, the designs formed by circles and so on. We also show that our unitals are inequivalent to the unitals derived from unitary polarities in the same shift planes. As designs, our unitals are also not isomorphic to the classical unitals (the Hermitian curves).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.