Pentagon capacity code ($\{(j,2j):j\in \mathbb{Z}/5\mathbb{Z}\}$)

These five words are independent in the strong square of the cycle graph $C_5$: a nonzero difference is a nonedge in the first or the second coordinate. A three-dimensional orthonormal representation with common vertical squared component $1/\sqrt{5}$ proves the matching upper bound. Consequently $c(C_5)=\vartheta (C_5)=\sqrt{5}$.