Complex valued sequences of length n are considered. A sequence is said to be aperfect sequence if all the out-of-phase periodic autocorrelation coefficients are equal to zero. For unrestricted sequences, a complete description of the set of perfect sequences is given. A sequence is said to be a phase shift keyed (PSK) sequence if all the coordinates are on the unit circle. A partial classification of perfect PSK sequences is presented. For prime lengths, it is shown that the number of essentially different perfect sequences is finite. For square free lengths, the number of essentially different perfect sequences is also finite. For lengths which are equal to a power of a prime, the dimension of the set of essentially different perfect sequences is found. General constructions of perfect sequences are presented. For the general case, the dimension of the set of essentially different perfect sequences is found.
展开▼
