Nearly perfect Gaussian integer sequences with arbitrary degree

Based on p-ary pseudorandom sequences, this study proposes a construction of degree-k Gaussian integer sequences of period N=k(p<^>m-1)/(p-1) N=k(pm-1)/(p-1) by utilising kth power residue symbol satisfying k|(p-1)(p-1), where p is an odd prime and positive integers m,k . The periodic autocorrelation values are 0 at shifts (N/k)) of the resultant sequences. Specially, there is exactly one non-zero out-of-phase periodic autocorrelation value of the resultant sequences for k=2. The non-zero elements of the sequences are balanced and can be predefined flexibly. Moreover, the maximum energy efficiency of the proposed sequences is close to (p-1)/p (p-1)/p for sufficiently large m.