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In [3], a universal linear algebraic model was proposed for describing homogeneous conformal geometries, such as the spherical, Euclidean, hyperbolic, Minkowski, anti-de Sitter and Galilei planes ([6]). This formalism was independent from the underlying field, providing an extension and general approach to other fields, such as finite fields. Some steps were taken even for the characteristic 2 case.

In this article, we undertake the study of the characteristic 2 case in more detail. In particular, the concept of virtual quadratic spaces is used ([4]), and a similar result is achieved for finite fields of characteristic 2 as for other fields. Some differences from the non-characteristic 2 case are also pointed out.

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