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

作者：Yu Nam Yul^*; Gong Guang

来源：IEEE Transactions on Information Theory, 2010, 56(12): 6376-6387.

DOI：10.1109/TIT.2010.2079590

• Correlation
• multiplicative characters
• polyphase sequences
• power residue sequences
• sequence family
• Sidelnikov sequences
• Weil bound

Power residue and Sidelnikov sequences are polyphase sequences with low correlation and variable alphabet sizes, represented by multiplicative characters. In this paper, sequence families constructed from the shift and addition of the polyphase sequences are revisited. Initially, psi(0) = 1 is assumed for multiplicative characters psi to represent power residue and Sidelnikov sequences in a simple form. The Weil bound on multiplicative character sums is refined for the assumption, where the character sums are equivalent to the correlations of sequences represented by multiplicative characters. General constructions of polyphase sequence families that produce some of known families as the special cases are then presented. The refined Weil bound enables the efficient proofs on the maximum correlation magnitudes of the sequence families. From the constructions, it is shown that M-ary known sequence families with large size can be partitioned into (M + 1) disjoint subsequence families with smaller maximum correlation magnitudes. More generalized constructions are also considered by the addition of multiple cyclic shifts of power residue and Sidelnikov sequences.

• 出版日期2010-12