Partial classification of sequences with perfect auto-correlation and bent functions

Complex valued sequences of length n are considered. A sequence is said to be a perfect sequence if all the out-of-phase periodic autocorrelation coefficients are equal to zero. A sequence is said to be a phase shift keyed (PSK) sequence if all the coordinates are on the unit circle. A sequence is said to be a polyphase sequence if all the coordinates are n'th roots of unity. For the case n is a power of a prime integer, the partial classification of perfect PSK sequences is given. As a consequence, the full classification of one dimensional bent functions is presented.