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A method of generating phase shift pulse codes of arbitrarily long length with zero periodic correlation except for the peak for zero shift is presented. The codes are of length where is any prime number, and different phase shifts corresponding to the th roots of unity are necessary to generate them. Since different phase shifts are required, these codes are not as easy to generate and process as the binary codes, but this does not seem to be a serious limitation to their usefulness. Application of these codes can be made as interpulse phase modulation for range resolution in pulse Doppler radars or for a method of synchronizing a pulse code communication system.