One-step completely orthogonalizable codes from generalized quadrangles

Abstract

For q any power of two, the dual D_q of the binary linear code spanned by the lines of the regular (q,q)-generalized quadrangle W(q) is shown to be a q-error correcting one-step completely orthogonalizable code of length q³ + q² + q + 1. By a previous result (Bagchi and Sastry, 1987, Geom. Dedicata 22, 137-147), the rate of D_q is at least half in the limit as q→∞. We also determine the full automorphism group and maximum weight of D_q and the minimum weight of its dual.