The second-order correlation measure of Zadoff-Chu sequences

For an integer r ≥ 1, the rth-order correlation measure (or the correlation measure of order r) of a sequence was introduced in cryptography as a measure of immunity against correlation attacks. When r = 2, it can be viewed as the maximum value in a subset of magnitudes of partial-period autocorrelation for a given sequence. In this paper, we determine the second-order correlation measure of Zadoff-Chu sequences of any period and show that it is invariant to the design parameter for them.