Multiplicative Characters, the Weil Bound, and Polyphase Sequence Families With Low Correlation

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Executive Summary

Sequences with low correlation find many applications in wireless communications for acquiring the correct timing information and distinguishing multiple users or channels with low mutual interference. It is desirable that sequences have variable alphabet sizes for adaptive modulation schemes which allow variable data rates in wireless systems according to channel characteristics. In addition, a large number of distinct sequences are also required for supporting as many distinct users or channels as possible. Power residue and Sidelnikov sequences introduced are polyphase sequences with low correlation and variable alphabet sizes, represented by multiplicative characters.

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