In wireless communication, the minimum Euclidean distance between codewords is a major factor for the ability to correct errors in messages, and it is of interest to maximize the minimum Euclidean distance. The thesis improves previously established general upper bounds on minimum Euclidean distance of phase shift keying block codes. There are no requirements on structure of codes, as the bound depends only on alphabet size, word length and code size. Prior to this thesis, bounds found by use of a method of Elias, had been improved by generalization of Elias' method. The method used here is an attempt to optimize that generalization.