A class of almost r-phase sequences with ideal autocorrelation

Shenghua Li, Lianfei Luo, Hannuo Zhao


For an odd prime N 1 (mod r), (r) almost r-phase sequences of period N areconstructed based on cyclotomy, where r is a positive integer and is Euler’sfunction. The new sequences have ideal autocorrelation property. Moreover, thesealmost r-phase sequences are modified to obtain r (r) r-phase sequences withgood autocorrelation, which include known polyphase power-residue sequences,Legendre sequences (r 2) and quadriphase sequences (r 4). The autocorrelationdistribution of these r-phase sequences are determined completely.


Almost r-phase sequence; correlation distribution; cyclotomic class; cyclotomic number; ideal autocorrelation.

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