Abstract
Let m be a positive integer, r ≡ 1 (mod 3) be a prime number, and the order of p modulo rm be \(\frac {\phi (r^{m})}3\), where ϕ is the Euler function. Let \(q=p^{\frac {\phi (r^{m})}3}\) and \(d=\frac {q-1}{r^{m}}\). We investigate the cross correlation distribution between a p-ary m-sequence and its d-decimated sequences. In this paper, we deal with the cases of p = 2 and p = 3. Our results show that the binary sequences have two-valued cross correlations and the ternary sequences have at most three-valued cross correlations, see Theorems 3.2 and 4.2. As a byproduct, we also explicitly compute the Gauss periods \(\eta _{0}^{(\frac {q-1}{r^{m}},q)}\).
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The paper is supported by National Natural Science Foundation of China (No. 61772015) and the Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-17-010)
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Wu, Y., Yue, Q., Shi, X. et al. Binary and ternary sequences with a few cross correlations. Cryptogr. Commun. 12, 511–525 (2020). https://doi.org/10.1007/s12095-019-00376-4
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DOI: https://doi.org/10.1007/s12095-019-00376-4