Abstract projective plane

Fano plane

The Fano plane is an Abstract projective plane and Galois geometry $P G (2, 2) = P (ℤ 32)$ . #m/def/geo/fin In addition it forms the unique Steiner system $S (2, 3, 7)$ , where lines are triads.

The Fano plane is shares an intimate relationship with the $[7, 4, 3] 2$ Hamming code.

Properties

$P G L (3, 2) ≅ P G L (1, 7)$ ¹

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1988. Geometry of the Mathieu groups and Golay codes ↩