Finite fields
Generators and irreducible polynomials over finite fields
Mathematics of Computation
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
New M-ary sequence families with low correlation and large size
IEEE Transactions on Information Theory
Large families of quaternary sequences with low correlation
IEEE Transactions on Information Theory
Improved binary codes and sequence families from Z4-linear codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A new binary sequence family with low correlation and large size
IEEE Transactions on Information Theory
Cross Correlation of Sidel'nikov Sequences and Their Constant Multiples
IEEE Transactions on Information Theory
New Families of -Ary Sequences With Low Correlation Constructed From Sidel'nikov Sequences
IEEE Transactions on Information Theory
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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, ψ(0) is assumed for multiplicative characters ψ 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.