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.
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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)
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© 2007 Springer-Verlag Berlin Heidelberg
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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
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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
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