Further results on degree‐2 perfect Gaussian integer sequences

Abstract

A complex number whose real and imaginary parts are both integers is called a Gaussian integer . A Gaussian integer sequence is said to be perfect if it has an ideal periodic autocorrelation function (PACF) where all out‐of‐phase values are zero. Further, the degree of a Gaussian integer sequence is defined as the number of distinct non‐zero Gaussian integers within one period of the sequence. Recently, the perfect Gaussian integer sequences have been found important practical applications as signal processing tools for orthogonal frequency‐division multiplexing systems. The present article generalises the authors’ earlier paper by Lee et al. (2015) related to the Gaussian integer sequences with ideal PACFs. By the applications of two‐tuple‐balanced binary sequences and cyclic difference sets, a number of new degree‐2 perfect Gaussian integer sequences with different periods are obtained.