New and Updated Semidefinite Programming Bounds for Subspace Codes

Abstract

We show that $A_2(7,4)\le 388$ and, more generally, $A_q(7,4)\le (q^2-q+1)[7{]}_q+q^4-2q^3+3q^2-4q+4$ by semidefinite programming for $q\le 101$. Furthermore, we extend results by Bachoc et al. on SDP bounds for $A_2(n,d)$, where $d$ is odd and $n$ is small, to $A_q(n,d)$ for small $q$ and small $n$.