Quaternionic line-sets and quaternionic Kerdock codes Original Research Article

When n is even, orthogonal spreads in an orthogonal vector space of type O−(2n−2,2) are used to construct line-sets of size (2n−1+1)2n−2 in H2n−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.