Abstract
Pseudorandom sequences have a wide applications. In stream ciphers, the key stream usually is a pseudorandom sequence over a finite field F q :
This work is partly supported by NSFC (Grant No. 60473025 and 90604011).
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References
Massey, J.L.: Shift-register synthesis and BCH decoding. IEEE Trans. Information Theory 15, 173–180 (1969)
Mills, W.H.: Continued fractions and linear recurrences. Math. Computation 29(129), 173–180 (1975)
Lasjaunias, A.: Diophantine approximation and continued fraction expansions of algebraic power series in positive characteristic. J. Number Theorey 65, 206–225 (1997)
Jones, W.B., Thron, W.J.: Continued fractions, analytic theory and applications. In: Rota, G. (ed.) Encyclopedia of Mathematics and Its Applications, vol. 11
Schmidt, W.M.: On continued fraction and diophantine approximation in power series fields. Acta Arith. 95, 139–166 (2000)
Bernstein, L.: The Jacobi-Perron algorithm: its theory and application. In: LNM207. Springer, Berlin (1971)
Podsypanin, E.V.: A generalization of continued fraction alogrithm that is related to ViggoBorun algorithm (Russian). Studies in Number Theory (LOMI), Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov 67 4, 184–194 (1977)
Ito, S., Keane, M., Ohtsuki, M.: Almost everywhere exponential convergence of the modified Jocobi-Perron algorithm. Ergod.Th. & Dynam. Sys. 13, 319–334 (1993)
Ito, S., Fujii, J., Higashino, H., Yasutomi, S.-I.: On simultaneous approximation to (α, α 2) with α 3 + kα− 1 = 0. J. Number Theory 99, 255–283 (2003)
Meester, R.: A Simple proof of the exponential convergence of the modified Jacobi-Perron algorithm. Ergod.Th. &Dynam. Sys. 19, 1077–1083 (1999)
Feng, K., Wang, F.: The Jacobi-Perron algorithm on function fields. Algebra Colloq. 1(2), 149–158 (1994)
Inoue, K.: On the exponential convergence of Jacobi-Perron algorithm over F(x)d. JP Journal of Algebra, Number Theory and Application 1(3), 27–41 (2003)
Dai, Z.D., Wang, K.P., Ye, D.F.: m-Continued fraction expansions of multi-Laurent series. ADVANCE IN MATHEMATICS(CHINA) 33(2), 246–248 (2004)
Dai, Z.D., Wang, K.P., Ye, D.F.: Multi-continued fraction algorithm on multi-formal Laurent Series. ACTA ARITHMETICA, 1–21 (2006)
Dai, Z.D., Jiang, S.Q., Imamura, K., Gong, G.: Asymptotic behavior of normalized linear complexity of ultimately non-periodic binary sequences. IEEE Trans. Infor. Theory 50, 2911–2915 (2004)
Dai, Z.-D., Imamura, K., Yang, J.-H.: Asymptotic behavior of normalized linear complexity of multi-sequences. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 129–142. Springer, Heidelberg (2005)
Dai, Z.-D., Feng, X., Yang, J.-H.: 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.D., Yang, J.H.: Multi-continued fraction algorithm and generalized B-M algorithm over F q . Finite Fields and Their Application (accepted)
Xing, C.: Multi-sequences with almost perfect linear complexity profile and function fields over finite fields. Journal of Complexity 16, 661–675 (2000)
Niederreiter, H.: Some computable complexity measure for binary sequences. In: Sequences and Their Applications, pp. 67–78. Springer, London (1999)
Wang, L.P., Niederreiter, H.: Enumeration results on the joint linear complexity profile of multisequences, Finite Fields and Their Application, doi:10.1016/j.ffa.2005.03.005
Niederreiter, H., Wang, L.-P.: Proof of a conjecture on the joint linear complexity profile of multisequences. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 13–22. Springer, Heidelberg (2005)
Feng, X.T., Wang, Q.L., Dai, Z.D.: Multi-sequences with d-perfect property. Journal of Complexity 21(2), 230–242 (2005)
Dai, Q.L., Dai, Z.D.: A proof that JPA and MJPA on multi-formal Layrent series can not garrentee the optimal rational approximation. Journal of the Graduate School of the Chinese Academy of Science (in Chinese) 22, 51–58 (2005)
Feng, X., Dai, Z.-D.: Expected value of the linear complexity of two-dimensional binary sequences. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 113–128. Springer, Heidelberg (2005)
Dai, Z.D., Feng, X.T.: Expected value of the normalized linear complexity of multi-sequences over the binary fields (preprint)
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Dai, Z. (2006). Multi-Continued Fraction Algorithms and Their Applications to Sequences. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_3
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DOI: https://doi.org/10.1007/11863854_3
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