Bounds on subspace codes based on totally isotropic subspaces in unitary spaces

Abstract

In this paper, the Sphere-packing bound, Singleton bound, Wang–Xing–Safavi-Naini bound, Johnson bound and Gilbert–Varshamov bound on the subspace codes [Formula: see text] based on [Formula: see text]-dimensional totally isotropic subspaces in unitary space [Formula: see text] over finite fields [Formula: see text] are presented. Then, we prove that [Formula: see text] codes based on [Formula: see text]-dimensional totally isotropic subspaces in unitary space [Formula: see text] attain the Wang–Xing–Safavi-Naini bound if and only if they are certain Steiner structures in [Formula: see text].