AUTHORS: Vladimir Edemskiy
Download as PDF
ABSTRACT: This paper examines the linear complexity of new generalized cyclotomic binary sequences of period 2p n recently proposed by Yi Ouang et al. (arXiv:1808.08019v1 [cs.IT] 24 Aug 2018). We generalize results obtained by them and discuss author’s conjecture of this paper
KEYWORDS: Binary sequences, linear complexity, cyclotomy
REFERENCES:
[
1] A. Akbary and S. Siavashi, The largest known
Wieferich numbers, Integers 18-A3, 2018,
pp. 1–6.
[2] T. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, North-Holland mathematical library. Elsevier 2004.
[3] F.G. Dorais and D. Klyve, A Wieferich prime
search up to 6.7 × 1015
, Journal of Integer Sequences, 14(11.9.2),2011, pp. 1–14.
[4] V. Edemskiy, C. Li, X. Zeng and T. Helleseth,
The linear complexity of generalized cyclotomic
binary sequences of period p
n
, Des. Codes Cryptography, pp. 1-15. //DOI: 10.1007/s10623-018-
0513-2
[5] K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, Graduate Texts
in Mathematics, Springer 1990.
[6] Y. Ouyang and X. Xie, Linear complexity
of generalized cyclotomic sequences of period
2p
m, arXiv:1808.08019v1
[cs.IT] 24 Aug 2018
[7] Z. Ye, P. Ke and C. Wu, A further study
of the linear complexity of new binary cyclotomic sequence of length p
n
. AAECC ,2018,
https://doi.org/10.1007/s00200-018-0368-9
[8] X. Zeng, H. Cai, X. Tang and Y. Yang,
Optimal frequency hopping sequences of odd
length. IEEE Transactions on Information Theory, 59(5), 2013, pp. 3237–3248 (2013).
[9] Z. Xiao, X. Zeng, C. Li and T. Helleseth, New
generalized cyclotomic binary sequences of period p
2
. Des. Codes Cryptography, 86(7), 2018,
pp. 1483-1497.
