Nordstrom–Robinson code and A7-geometry

The Nordstrom–Robinson code NR is a nonlinear binary code of length 16, with 28 codewords and minimum distance 6. Its automorphism group is a semidirect product of an elementary abelian group of order 16 and the alternating group A7. This group and the corresponding action of A7 is also at the origin of the sporadic A7-geometry. We construct this geometry and derive the Nordstrom–Robinson code from it.