Quaternionic line-sets and quaternionic Kerdock codes

Abstract

When n is even, orthogonal spreads in an orthogonal vector space of type O −(2 n−2,2) are used to construct line-sets of size (2 n−1 +1)2 n−2 in H 2 n−2 all of whose angles are 90° or cos −1(2 −(n−2) 2 ) . These line-sets are then used to obtain quaternionic Kerdock codes. These constructions are based on ideas used by Calderbank, Cameron, Kantor, and Seidel in real and complex spaces.