On the k-Error Linear Complexity of p^ -Periodic Binary Sequences

In this correspondence, we study the statistical stability properties of p m -periodic binary sequences in terms of their linear complexity and k-error linear complexity, where p is n prime number and 2 is a primitive root modulo p 2 . We show that their linear complexity and k-error linear complexi...

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Bibliographic Details
Published in:IEEE transactions on information theory 2007-06, Vol.53 (6), p.2297-2304
Main Authors: Han, Yun Kyoung, Chung, Jin-Ho, Yang, Kyeongcheol
Format: Article
Language:English
Subjects:
Binary sequences
Binary system
Cryptography
Electrical engineering
Electronics
Galois fields
Hamming weight
Information systems
Information technology
k -error linear complexity
linear complexity
Microwave integrated circuits
OFDM
Optical wavelength conversion
periodic sequences
Polynomials
Random sequences
Stability
stream ciphers
XWLI algorithm
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Summary:In this correspondence, we study the statistical stability properties of p m -periodic binary sequences in terms of their linear complexity and k-error linear complexity, where p is n prime number and 2 is a primitive root modulo p 2 . We show that their linear complexity and k-error linear complexity take a value only from some specific ranges. We then present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity in a new viewpoint different from the approach by Meidl. We also derive the distribution of p m -periodic binary sequences with specific k-error linear complexity. Finally, we get an explicit formula for the expectation value of the k-error linear complexity and give its lower and upper bounds, when k les [p/2].
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2007.896863