Abstract
In this paper, a large family \({\mathcal{F}^k(l)}\) of binary sequences of period 2n − 1 is constructed for odd n = 2m + 1, where k is any integer with gcd(n, k) = 1 and l is an integer with 1 ≤ l ≤ m. This generalizes the construction of modified Gold sequences by Rothaus. It is shown that \({\mathcal{F}^k(l)}\) has family size \({2^{ln}+2^{(l-1)n}+\cdots+2^n+1}\), maximum nontrivial correlation magnitude 1 + 2m+l. Based on the theory of quadratic forms over finite fields, all exact correlation values between sequences in \({\mathcal{F}^k(l)}\) are determined. Furthermore, the family \({\mathcal{F}^k(2)}\) is discussed in detail to compute its complete correlation distribution.
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Communicated by T. Helleseth.
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Zhou, Z., Tang, X. Generalized modified Gold sequences. Des. Codes Cryptogr. 60, 241–253 (2011). https://doi.org/10.1007/s10623-010-9430-8
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DOI: https://doi.org/10.1007/s10623-010-9430-8