A Construction for Perfect Periodic Autocorrelation Sequences

There exists a number of known constructions for perfect sequences over roots of unity. These include Frank sequences of length n over n roots of unity [Heimiller, 1961][Frank, 1962], Chu sequences of length n over n roots of unity for n odd and length n over 2n roots of unity for n even [Chu, 1972], Milewski sequences of length m overm roots of unity [Milewski, 1983], Liu-Fan sequences of length n over n roots of unity for n even [Liu, 2004]. Other sequence constructions exist [Ipatov, 1979][Alltop, 1980][Lewis, 1982][Kumar, 1985] [Gabidulin, 1993][Mow, 1993]. This construction presented in this paper is similar to the ZCZ sequence construction by the authors [Blake, 2012].