Kerdock spherical-code optimality conjecture

For each integer $k e 0$, let a Kerdock spherical code be the spherical code in $\mathbb{R}^{2^{2k}}$ constructed from the Kerdock binary code, with $2^{4k}+2^{2k+1}$ points and maximal inner product $1/2^k$. Kerdock spherical-code optimality conjecture. Three-point bounds prove optimality for Kerdock spherical codes in each dimension $2^{2k}$ with $k \ge 2$, and hence also for the corresponding Kerdock binary codes. The cases $2\le k\le5$ are proved in the paper; the conjecture concerns all $k\ge2$, while the case $k=1$ appears to require different methods.