Abstract: Due to its good correlation property, perfect Gaussian integer sequence has been widely used in modern communication system. However, the known construction methods for perfect Gaussian integer sequence is limited. In this paper, we present a new construction method for perfect Gaussian integer sequences with their period being the square of an odd prime. Based on the generalized cyclotomy of order 2 over the ring of integers with modulo being an odd prime square, we construct Gaussian integer sequence with the period being an odd prime square and determine its autocorrelation function distributions. Furthermore, the construction of perfect Gaussian integer sequence is proved to be equivalent to the solution of an equation system of degree 2 over complex field. Special cases of above equation system are then considered.

Key words: Gaussian integer, perfect sequence, generalized cyclotomy, autocorrelation function