Symmetric 2-adic complexity of Hall generalized cyclotomic sequences
https://doi.org/10.34680/2076-8052.2023.5(134).700-707
Abstract
We study the symmetric 2-adic complexity of Hall generalized cyclotomic sequences whose period is equal to the power of a prime. Sequences are defined based on generalized cyclotomic classes. It is shown that the considered sequences have high symmetric 2-adic complexity. The research method uses generalized Gaussian periods.
About the Authors
V. A. Edemskiy
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
V. V. Gavrushko
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
V. M. Petrov
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
References
1. Goresky M., Klapper A. Algebraic Shift Register Sequences. Cambridge University Press, 2012. 498 p.
2. Xiong H., Qu L., Li C. A new method to compute the 2-adic complexity of binary sequences // IEEE Transactions on Information Theory. 2014. 60(4). 2399-2406. DOI: 10.1109/TIT.2014.2304451
3. Hu H. Comments on “A new method to compute the 2-adic complexity of binary sequences” // IEEE Transactions on Information Theory. 2014. 60(9). 5803-5804. DOI: 10.1109/TIT.2014.2336843
4. Zhang L., Zhang J., Yang M., Feng K. On the 2-adic complexity of the Ding-Helleseth-Martinsen binary sequences // IEEE Transactions on Information Theory. 2020. 66(7). 4613-4620. DOI: 10.1109/TIT.2020.2964171
5. Hu H., Feng D. On the 2-adic complexity and the k-error 2-adic complexity of periodic binary sequences // IEEE Transactions on Information Theory. 2008. 54(2). 874-883. DOI: 10.1109/TIT.2007.913238
6. Xiao Z., Zeng X., Ke M. On the symmetric 2-adic complexity of periodic binary sequences // Advances in Mathematics of Communications. 2022. DOI: 10.3934/amc.2022088
7. Sun Y., Yan T., Chen Z., Wang L. The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude // Cryptography and Communications. 2020. 12(3). 675-683. DOI: 10.1007/s12095-019-00411-4
8. Sun F., Yue Q., Li X. On the 2-adic complexity of cyclotomic binary sequences of order four // Applicable Algebra in Engineering Communication and Computing (AAECC). 2023. DOI: 10.1007/s00200-023-00598-3
9. Sun F., Yue Q., Li X. On the 2-adic complexity of cyclotomic binary sequences of order three // Advances in Mathematics of Communications. 2022. 16(4). 985-999. DOI: 10.3934/amc.2022049
10. Xiao Z., Zeng X., Sun Z. 2-Adic complexity of two classes of generalized cyclotomic binary sequences // International Journal of Foundations of Computer Science. 2016. 27(7). 879-893. DOI: 10.1142/s0129054116500350
11. Edemskiy V. A., Koltsova S. A. Symmetric 2-adic complexity of generalized cyclotomic sequences of order six with period pn // Journal of Physics: Conference Series. 2021. 2052. 012009. DOI: 10.1088/1742-6596/2052/1/012009
12. Kim J.-H., Song H.-Y. On the linear complexity of Hall's sextic residue sequences // IEEE Transactions on Information Theory. 2001. 47(5). 2094-2096. DOI: 10.1109/18.930950
13. Hall M. Combinatorial Theory. Blaisdell, Waltham, MA, 1967. 310 p. (Russ. ed.: Kholl M. Kombinatorika. Moscow, Mir Publ., 1970. 424 p.)
14. Cusick T., Ding C., Renvall A. Stream Ciphers and Number Theory. North-Holland mathematical library. Elsevier, 2004. 474 p.
Review
For citations:
Edemskiy V.A., Gavrushko V.V., Petrov V.M. Symmetric 2-adic complexity of Hall generalized cyclotomic sequences. Title in english. 2023;(5(134)):700-707. (In Russ.) https://doi.org/10.34680/2076-8052.2023.5(134).700-707
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