Abstract
In this paper, the distribution of the shortest linear recurring sequences in Z /(p) is studied. It is found that the shortest linear recurrent length is always equal to n / 2 when n is even and is always equal to n / 2+1 when n is odd for any sequence whose length is n. In other words, the shortest linear recurring length is always equal to the half of the length of the given sequence. The probability of finding the distribution of the shortest linear recurring length of two sequences in Z / (p) field is also given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Meidl, W.: On the Stability of 2n-Periodic Binary Sequences. IEEE Trans. Inform Theory, IT-51(3), 1151–1155 (2005)
Reeds, J.A., Sloane, N.J.A.: Shift-register synthesis (modulo m). SIAM Journal on Computing 14(3), 505–513 (1985)
Dingfeng, Y., Zongduo, D.: Periodic sequence linear order of complexity under two marks replacing. In: Fourth session of Chinese cryptology academic conference collection (1996) (in Chinese)
Yujie, Z., Jinjun, Z.: The relationship between two kinds of sequences syntheses algorithm over ring Z/(m). In: Fifth session of Chinese cryptology academic conference collection (1998) (in Chinese)
Liying, G., Yuefei, Z.: The shortest linear recurrence of two sequences. Journal of information engineering university 2(1), 17–22 (2001) (in Chinese)
Guiliang, F., Tzeng, K.K.A.: Generalization of the Berlekamp-Massey algorithm for multi-sequence shift-register synthesis with applications to decoding cyclic codes. IEEE Trans. Inform. Theory 37(5), 1274–1287 (1991)
Guiliang, F., Tzeng, K.K.A.: Generalized Euclidean algorithm for multi-sequence shift-register synthesis. IEEE Trans. Inform. Theory 35(3), 584–594 (1989)
Jinjun, Z., Wenfeng, Q., Yujie, Z.: Gröbner base extension and Multi-sequences comprehensive algorithm over Z/(m). Science in China, 113–120 (1995) (in Chinese)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yin, Q., Luo, Y., Guo, P. (2005). Special Distribution of the Shortest Linear Recurring Sequences in Z /(p) Field. In: Hao, Y., et al. Computational Intelligence and Security. CIS 2005. Lecture Notes in Computer Science(), vol 3802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11596981_6
Download citation
DOI: https://doi.org/10.1007/11596981_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30819-5
Online ISBN: 978-3-540-31598-8
eBook Packages: Computer ScienceComputer Science (R0)