Geometric Hyperplanes of the Near Hexagon L_3 times GQ(2, 2)

Abstract

Having in mind their potential quantum physical applications, we classify all geometric hyperplanes of the near hexagon that is a direct product of a line of size three and the generalized quadrangle of order two. There are eight different kinds of them, totalling to 1023 = 2^{10} - 1 = |PG(9, 2)|, and they form two distinct families intricately related with the points and lines of the Veldkamp space of the quadrangle in question.

10 pages, 5 figures and 2 tables; Version 2 - more detailed discussion of the properties of hyperplanes

References in corpus (2)

• Black Hole Entropy and Finite Geometry
• Projective Ring Line Encompassing Two-Qubits

Cited by in corpus (5)

• Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
• The Veldkamp Space of the Smallest Slim Dense Near Hexagon
• Magic Three-Qubit Veldkamp Line and Veldkamp Space of the Doily
• Veldkamp Spaces of Low-Dimensional Ternary Segre Varieties
• A Classification of the Veldkamp Lines of the Near Hexagon L_3 times GQ(2, 2)