Abstract
The binary linear feedback shift register sequences of degree n and maximum period p = 2n − 1 (the m-sequences) are useful in numerous applications because, although deterministic, they satisfy a number of interesting “randomness properties”.
An important open question is whether a binary sequence of period p = 2n − 1 with both the span-n property and the two-level correlation property must be an m-sequence.
There is a direct correspondence between m-sequences of degree n and primitive polynomials of degree n over GF(2). Several conjectures are presented about primitive polynomials with a bounded number of terms.
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
Golomb, S.: Shift Register Sequences. Holden-Day Inc., San Francisco (1967); revised edition Aegean Park Press, Laguna Hills, CA (1982)
Golomb, S., Gong, G.: Signal Design for Good Correlation – for Wireless Communication, Cryptography, and Radar. Cambridge University Press, Cambridge (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Golomb, S.W. (2007). Periodic Binary Sequences: Solved and Unsolved Problems. In: Golomb, S.W., Gong, G., Helleseth, T., Song, HY. (eds) Sequences, Subsequences, and Consequences. Lecture Notes in Computer Science, vol 4893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77404-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-77404-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77403-7
Online ISBN: 978-3-540-77404-4
eBook Packages: Computer ScienceComputer Science (R0)