Generalized modified Gold sequences |
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Authors: | Zhengchun Zhou Xiaohu Tang |
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Institution: | 1.School of Mathematics,Southwest Jiaotong University,Chengdu,China;2.Provincial Key Lab of Information Coding and Transmission, Institute of Mobile Communications,Southwest Jiaotong University,Chengdu,China |
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Abstract: | In this paper, a large family \({\mathcal{F}^k(l)}\) of binary sequences of period 2 n ? 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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