Abstract
The sequence pairs of length \(2^{m}\) projected from Type-II and Type-III/II complementary array pairs of size \(2\times 2\times \cdots \times 2\) (m-times) form Type-II and Type-III complementary sequence pairs, respectively. An exhaustive search for binary Type-II and Type-III complementary sequence pairs of small lengths \(2^{m}\) (\(m=1,2,3,4\)) shows that they are all projected from the aforementioned complementary array pairs, whose algebraic normal forms satisfy specified expressions. It’s natural to ask whether the conclusion holds for all m. In this paper, we proved that these expressions of algebraic normal forms determine all the binary Type-II and Type-III/II complementary array pairs of size \(2\times 2\times \cdots \times 2\).
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The material in this paper was presented in part at The 10th International Workshop on Signal Design and its Applications in Communications (IWSDA’2022).
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The authors are supported in part by the National Natural Science Foundation of China under Grant 62172319 and Grant U19B2021; in part by the National Key Research and Development Program under Grant 2021YFA000503.
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The authors are supported in part by the National Natural Science Foundation of China under Grant 62172319 and Grant U19B2021; in part by the National Key Research and Development Program under Grant 2021YFA000503. The material in this paper was presented in part at The 10th International Workshop on Signal Design and its Applications in Communications (IWSDA’2022).
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Xue, E., Wang, Z. & Chai, J. Boolean functions of binary Type-II and Type-III/II complementary array pairs. Cryptogr. Commun. (2024). https://doi.org/10.1007/s12095-024-00701-6
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DOI: https://doi.org/10.1007/s12095-024-00701-6