Nearly perfect Gaussian integer sequences with arbitrary degree

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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 ) by utilising kth power residue symbol satisfying k | ( p − 1 ) , where p is an odd prime and positive integers m , k ≥ 2 . The periodic autocorrelation values are 0 at shifts τ ≢ 0 ( mod ( 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 for sufficiently large m.