Abstract
Let l be an odd prime with \(l\equiv 1\pmod 4\), \(N=l^m\) a positive integer, \({\text {ord}}_N(2)=f\), and \(q=2^f\), where \(f=\phi (N)/t\) and \(\phi (\cdot )\) is the Euler’s function. Let \(\{u_i\}=({\text {Tr}}_{q/2}(\omega ^i))_{i=0}^{q-2}\) be a binary sequence of period \(q-1\), where \(\omega \) is a primitive element of a finite field \(\mathbb F_{q}\). In this paper, we obtain two-valued cross correlation distributions between two sequences \(\{u_i\}\) and their \(\frac{q-1}{N}\)-decimation sequences in two cases: \(t=2\) and \(t=4\).
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The authors are very grateful to the reviewers and the Editor for their valuable suggestions that much improved the quality of this paper.
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The paper was supported by National Natural Science Foundation of China under Grants 12171420, 62172219, and Foundation of QingTan scholars of Zaozhuang University.
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Li, F., Yue, Q. & Liu, F. Two-valued cross correlation distributions between binary m sequences and their decimation sequences. AAECC 34, 1013–1025 (2023). https://doi.org/10.1007/s00200-021-00535-2
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DOI: https://doi.org/10.1007/s00200-021-00535-2