Analysis and design of stream ciphers
Analysis and design of stream ciphers
The characterization of 2n-periodic binary sequences with fixed 1-error linear complexity
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
A relationship between linear complexity and k-error linear complexity
IEEE Transactions on Information Theory
On the stability of 2n-periodic binary sequences
IEEE Transactions on Information Theory
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The linear complexity of sequences is an important measure to gauge the cryptographic strength of key streams used in stream ciphers. The instability of linear complexity caused by changing a few symbols of sequences can be measured using k-error linear complexity. In their SETA 2006 paper, Fu, Niederreiter, and Su [3] studied linear complexity and 1-error linear complexity of 2n-periodic binary sequences to characterize such sequences with fixed 1-error linear complexity. In this paper we study the linear complexity and the k-error linear complexity of 2n-periodic binary sequences in a more general setting using a combination of algebraic, combinatorial, and algorithmic methods. This approach allows us to characterize 2n-periodic binary sequences with fixed 2-error or 3-error linear complexity L, when the Hamming weight of the binary representation of 2n茂戮驴 Lis $w_H(2^n-L) \neq 2$. Using this characterization we obtain the counting function for the number of 2n-periodic binary sequences with fixed k-error linear complexity Lfor k= 2 and 3 when $w_H(2^n-L) \neq 2$.