New classes of sequence families with low correlation by using multiplicative and additive characters

Abstract

For an odd prime p, a new sequence family of period p^m-\mathrm{1}, size \left(M-\mathrm{1}\right)p^{mr} is proposed using multiplicative and additive characters. The upper bound for the maximum magnitude of nontrivial correlations of the sequence family is derived using well-known character sums. The upper bound is shown to be \left(r+\mathrm{1}\right)\sqrt{p^m}+\mathrm{3}, which meets the Welch bound asymptotically.

Keywords

finite field / character sum / correlation / polyphase sequence / Welch bound

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Higher Education Press and Springer-Verlag Berlin Heidelberg