On some binary codes from orthogonal geometry of characteristic two

Abstract

In their natural primitive rank-3 action on the singular and non-singular points of the projective space of dimension 2m − 1, the simple orthogonal groups O ^ε _2m (F₂), for ε = ±1 and m ≥ 3 have 2-modular representations that give rise to self-orthogonal binary codes whose properties can be linked to those of the underlying geometry. We describe the structures of the stabilizers of the codewords of any given non-zero weight in the codes. Moreover we show that the codewords of any given non-zero weight are single orbits stabilized by maximal subgroups of the orthogonal groups.