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Designs, Codes and Cryptography

Erschienen in:

04.05.2019

Linear complexity of generalized cyclotomic sequences of period $2p^{m}$

verfasst von: Yi Ouyang, Xianhong Xie

Erschienen in: Designs, Codes and Cryptography | Ausgabe 11/2019

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Abstract

In this paper, we construct two generalized cyclotomic binary sequences of period $2p^{m}$ based on the generalized cyclotomy and compute their linear complexity, showing that they are of high linear complexity when $m\ge 2$.

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Bai E., Liu X., Xiao G.: Linear complexity of new generalized cyclotomic sequences of order two of length $pq$. IEEE Trans. Inf. Theory 51(5), 1849–1853 (2005).MathSciNetCrossRef

Chang Z., Li D.: On the linear complexity of generalized cyclotomic binary sequence of length $2pq$. Concurr. Comput. Pract. Exp. 26(8), 1520–1530 (2014).CrossRef

Cusick T., Ding C., Renvall A.: Stream Ciphers and Number Theory. North-Holland Mathematical Library, vol. 55, pp. 198–212. Elsevier, Amsterdam (1998).MATH

Ding C.: Binary cyclotomic generators. Fast Software Encryption. LNCS, vol. 1008, pp. 29–60. Springer, Leuven (1995).CrossRef

Ding C.: Linear complexity of generalized cyclotomic binary sequences of order $2$. Finite Fields Appl. 3, 159–174 (1997).MathSciNetCrossRef

Ding C., Helleseth T.: New generalized cyclotomy and its applications. Finite Fields Appl. 4, 140–166 (1998).MathSciNetCrossRef

Ding C., Helleseth T.: Generalized cyclotomy codes of length $p_{1}^{m_{1}}p_{2}^{m_{2}}\cdots p_{t}^{m_{t}}$. IEEE Trans. Inf. Theory 45(2), 467–474 (1999).CrossRef

Edemskiy V.: About computation of the linear complexity of generalized cyclotomic sequences with period $p^{n+1}$. Des. Codes Cryptogr. 61, 251–260 (2011).MathSciNetCrossRef

Edemskiy V., Li C., Zeng X., Helleseth T.: The linear complexity of generalized cyclotomic binary cyclotomic sequences of period $p^{n}$. Des. Codes Cryptogr. (2018). https://doi.org/10.1007/s10623-018-0513-2.CrossRefMATH

10.

Golomb S.W.: Shift register sequence. Holden Day, San Francisco (1967).

11.

Hu H.G., Gong G.: New sets of zeros or low correlation zone sequences via interleaving technique. IEEE Trans. Inf. Theory 56, 1702–1713 (2010).MathSciNetCrossRef

12.

Hu L., Yue Q., Wang M.: The linear complexity of Whiteman’s generalized cyclotomic sequences of period $p^{m+1}q^{n+1}$. IEEE Trans. Inf. Theory 58, 5534–5543 (2012).MathSciNetCrossRef

13.

Ke P.H., Zhang J., Zhang S.Y.: On the of linear complexity and the autocorrelation of generalized cyclotomic binary sequences with the period $2p^{m}$. Des. Codes Cryptogr. 67(3), 325–339 (2013).MathSciNetCrossRef

14.

Kim Y. J., Song H. Y.: Linear complexity of prime $n$-square sequences. In: IEEE International Symposium on Information Theory, Toronto, Canada, pp. 2405–2408 (2008).

15.

Kim Y.J., Jin S.Y., Song H.Y.: Linear complexity and autocorrelation of prime cube sequences. LNCS, vol. 4851, pp. 188–197. Springer, Berlin (2007).

16.

Li D.D., Wen Q.Y.: Linear complexity of generalized cyclotomic binary sequences with period $2p^{m+1}q^{n+1}$. IEICE Trans. Fund. Electron. E 98A, 1244–1254 (2015).CrossRef

17.

Liu F., Peng D.Y., Tang X.H.: On the autocorrelation and the linear complexity of $q$-ary prime $n$-square sequence. Sequences and Their Applications. LNCS, vol. 6338, pp. 139–150. Springer, Berlin (2010).

18.

Park Y.H., Hong D., Chun E.: On the linear complexity of some generalized cyclotomic sequences. Int. J. Algebra Comput. 14(4), 431–439 (2004).MathSciNetCrossRef

19.

Whiteman A.L.: A family of difference sets. Illionis J. Math. 6(1), 107–121 (1962).MathSciNetCrossRef

20.

Xiao Z.B., Zeng X.Y., Li C.L., Helleseth T.: New generalized cyclotomic binary sequences of period $p^{2}$. Des. Codes Cryptogr. 86, 1483–1497 (2018).MathSciNetCrossRef

21.

Yan T.: Some notes on the generalized cyclotomic binary sequences of length $2p^{m}$ and $p^{m}$. IEICE Trans. Fund. E96–A 10, 2049–2051 (2013).CrossRef

22.

Yan T., Sun R., Xiao G.: Autocorrelation and linear complexity of the new generalized cyclotomic sequences. IEICE Trans. Fund. Electron. E90–A, 857–864 (2007).CrossRef

23.

Ye Z.F., Ke P.H., Wu C.H.: A further study on the linear complexity of new binary cyclotomic sequence of length $p^{r}$. arXiv:1712.08886V2 [cs.CR] 15 Mar 2018.

24.

Zeng X., Cai H., Tang X., Yang Y.: Optimal frequency hopping sequences of odd length. IEEE Trans. Inf. Theory 59(5), 3237–3248 (2013).MathSciNetCrossRef

25.

Zhang J.W., Zhao C.A., Ma X.: Linear complexity of generalized cyclotomic binary sequences of length $2p^{m}$. Applicable Algebra in Engineering, Communication and Computing, vol. 21, pp. 93–108. Springer, Berlin (2010).

Titel: Linear complexity of generalized cyclotomic sequences of period
verfasst von: Yi Ouyang
Xianhong Xie
Publikationsdatum: 04.05.2019
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 11/2019
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-019-00638-5

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Linear complexity of generalized cyclotomic sequences of period \(2p^{m}\)

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