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# A New Family of p -Ary Sequences of Period (p

IEEE Transactions on Information Theory (Impact Factor: 2.62). 01/2011; 57:3825-3830.
Source: DBLP

ABSTRACT For an odd prime p congruent to 3 modulo 4 and an odd integer n, a new family of p-ary sequences of period N = p 01 2 with low correlation is proposed. The family is constructed by shifts and additions of two decimated m-sequences with the decimation factors 2 and 2d; d = N 0p n01 . The upper bound for the maximum magnitude of nontrivial correlations of this family is derived using well known Kloosterman sums. The upper bound is shown to be 2 N + 1 2 = p 2p n , which is twice the Welch's lower bound and approximately 1.5 times the Sidelnikov's lower bound. The size of the family is 2(p n 01), which is four times the period of sequences.

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ABSTRACT: 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)=1 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.
IEEE Transactions on Information Theory 01/2011; · 2.62 Impact Factor
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