The problem of optimal antipodal codes can be framed as finding low rank Gram matrices $G$ with $G_{ ii} = 1$ and $|G_{ ij}| \leq \epsilon$ for $1 \leq i \neq j \leq n$. In 2018, Bukh and Cox introduced a new bounding technique by removing the condition that $G$ be a gram matrix. In this work, we investigate how tight this relaxation is, and find exact results for real valued matrices of rank $2$.
Categories: math.MG math.CO