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Nearly perfect Gaussian integer sequences with arbitrary degree

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 by utilising kth power residue symbol satisfying , where p is an odd prime and positive integers . The periodic autocorrelation values are 0 at shifts of the resultant sequences. Specially, there is exactly one non-zero out-of-phase periodic autocorrelation value of the resultant sequences for . 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 for sufficiently large m.

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