Optimal subspace codes in $\mathrm{PG}(4,q)$

Abstract

We investigate subspace codes whose codewords are subspaces of $\mathrm{PG}(4,q)$ having non-constant dimension. In particular, examples of optimal mixed-dimension subspace codes are provided, showing that ${\mathcal{A}}_q(5,3)=2(q^3+1)$.