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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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61102093 and 61072080), Natural Science Foundation of Fujian Province (No. 2010J01319), and Key Project of Fujian Provincial Universities — Information Technology Research Based on Mathematics.

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