Simplex (transorthogonal) signals are equally likely highly-corr

Simplex (transorthogonal) signals are equally likely highly-correlated signals with the most negative correlation that can be achieved with a set of M orthogonal signals. That is, the correlation coefficient between any pair of signals in the set is defined by below, one method of constructing simplex signals is to start with a set of M orthogonal signals, each with energy E, and then apply the minimum energy translate. Consider a set of three equally likely symbols whose signal constellation consists of the vertices of an equilateral triangle. Show that these three symbols constitute a simplexcode.