Chapter

# A General Approach to Construction and Determination of the Linear Complexity of Sequences Based on Cosets

09/2010; DOI:10.1007/978-3-642-15874-2_10 pp.125-138

ABSTRACT We give a general approach to N-periodic sequences over a finite field

\mathbb Fq\mathbb F_q constructed via a subgroup D of the group of invertible elements modulo N. Well known examples are Legendre sequences or the two-prime generator. For some generalizations of sequences considered
in the literature and for some new examples of sequence constructions we determine the linear complexity.

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• ##### Article:Linear complexity of new generalized cyclotomic sequences of order two of length pq
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ABSTRACT: In this correspondence, the linear complexity and minimal polynomial of new generalized cyclotomic sequences of order two are determined. Our results show that these sequences also have high linear complexity.
IEEE Transactions on Information Theory 06/2005; · 3.01 Impact Factor
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##### Article:Some notes on the two-prime generator of order 2
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ABSTRACT: The two-prime generator of order 2 has several desirable randomness properties if the two primes are chosen properly. In particular, Ding deduced exact formulas for the (periodic) autocorrelation and the linear complexity of these sequences. In this note, we analyze parts of the period of the two-prime generator of order 2 and obtain bounds on the aperiodic autocorrelation and linear complexity profile.
IEEE Transactions on Information Theory 11/2005; · 3.01 Impact Factor
• ##### Article:On the linear complexity of Legendre sequences
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ABSTRACT: We determine the linear complexity of all Legendre sequences and the (monic) feedback polynomial of the shortest linear feedback shift register that generates such a Legendre sequence. The result shows that Legendre sequences are quite good from the linear complexity viewpoint
IEEE Transactions on Information Theory 06/1998; · 3.01 Impact Factor

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### Keywords

invertible elements modulo N

linear complexity

N-periodic sequences

sequence constructions

sequences

subgroup D

two-prime generator