Investigations on Periodic Sequences With Maximum Nonlinear Complexity

Investigations on Periodic Sequences With Maximum Nonlinear Complexity

The nonlinear complexity of a periodic sequence s is the length of the shortest feedback shift register that can generate s, and its value is upper bounded by the least period of s minus 1. In this paper, a recursive approach that generates all periodic sequences with maximum nonlinear complexity is...

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Veröffentlicht in:IEEE transactions on information theory 2017-10, Vol.63 (10), p.6188-6198
Hauptverfasser: Zhimin Sun, Xiangyong Zeng, Chunlei Li, Helleseth, Tor
Format: Artikel
Sprache:eng
Schlagworte:
<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">k th-order complexity
Complexity
Complexity theory
Cryptography
Electronic mail
Games
nonlinear complexity
Periodic sequence
Recursive methods
Sequences
Shift registers
Sun
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Zusammenfassung:The nonlinear complexity of a periodic sequence s is the length of the shortest feedback shift register that can generate s, and its value is upper bounded by the least period of s minus 1. In this paper, a recursive approach that generates all periodic sequences with maximum nonlinear complexity is presented, and the total number of such sequences is determined. The randomness properties of these sequences are also examined.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2714681