Abstract
In this work, based on the technique of multi-continued fractions [6,7,8], we study the normalized expected value e(2,n) of the linear complexity of binary sequences of dimension 2. As a result, e(2,n) is determined, and moreover, it is found that \(e(2,n) \rightarrow \frac{2}{3}\) as n goes into infinity.
This work is partly supported by NSFC (Grant No. 60173016), and the National 973 Project (Grant No. 1999035804).
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References
Niederreiter, H.: Some computable complexity measures for binary sequences. In: Ding, C., Helleseth, T., Niederreiter, H. (eds.) Sequences and their applications, pp. 67–78. Springer, London (1999)
Rueppel, R.A.: Analysis and Design of Stream ciphers. Springer, Heidelberg (1986)
Dai, Z.D., Yang, J.H.: Linear complexity of periodically repeated random sequences. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 168–175. Springer, Heidelberg (1991)
Meidl, W., Niderreiter, H.: The expected value of joint linear complexity of periodic multisequences. Journal of Complexity 19, 61–72 (2003)
Xing, C.: Multi-sequences with Almost Perfect Linear Complexity Profile and Function Fields over Finite Fields. Journal of Complexity 16, 661–675 (2000)
Dai, Z., Wang, K., Ye, D.: m-Continued Fraction Expansions of Multi-Laurent Series. Advances In Mathematics (China) 33(2), 246–248 (2004)
Dai, Z., Wang, K., Ye, D.: Multidimensional Continued Fraction and Rational Approximation, http://arxiv.org/abs/math.NT/0401141
Dai, Z., Feng, X., Yang, J.: Multi-continued fraction algorithm and generalized B-M algorithm over F 2. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 339–354. Springer, Heidelberg (2005)
Dai, Z., Feng, X.: Multi-continued fraction algorithm and generalized B-M algorithm over F 2. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 113–117. Springer, Heidelberg (2005)
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Feng, X., Dai, Z. (2005). Expected Value of the Linear Complexity of Two-Dimensional Binary Sequences. In: Helleseth, T., Sarwate, D., Song, HY., Yang, K. (eds) Sequences and Their Applications - SETA 2004. SETA 2004. Lecture Notes in Computer Science, vol 3486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11423461_6
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DOI: https://doi.org/10.1007/11423461_6
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