Bounding the minimal Euclidean distance for any PSK block codes of alphabet size 8

We consider a bound for the minimal Euclidean distance of any PSK block code with eight symbols. The main result was established in [6] — here we prove that the bound is in fact stronger than was proven there. The bound is deduced by generalizing Elias' method of a critical sphere. It is not asympthotic, as previous Elias' sphere bounds, but valid for any specific word length and code size. Many known codes fulfil the bound with equality, proving the sharpness of the bound for these parameter values as well as the optimality of these codes.