Golay codes,Witt designs, and Leech lattice
Andries E. Brouwer, Hendrik Van Maldeghem · Cambridge University Press eBooks · 2022
In this chapter we construct the Golay codes and the Witt designs, both in several ways. The uniqueness is proved in a self-contained way for the binary case; in the ternary case some details are left out. We then study the associated Witt designs, which are remarkable Steiner systems on 12 and 24 points. We show uniqueness of these, and of the (multiply) derived designs. We define the two standard near polygons from the ternary Golay code and the large Witt design. We discuss the geometry of the projective plane of order 4 providing an alternative construction and uniqueness proof of the Witt designs. Finally, we introduce the Leech lattice and its binary and complex variants.