Elsevier

Journal of Complexity

Volume 18, Issue 1, March 2002, Pages 87-103
Journal of Complexity

Regular Article
Linear Complexity, k-Error Linear Complexity, and the Discrete Fourier Transform

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Abstract

Complexity measures for sequences of elements of a finite field play an important role in cryptology. We focus first on the linear complexity of periodic sequences. By means of the discrete Fourier transform, we determine the number of periodic sequences S with given prime period length N and linear complexity LN, 0(S)=c as well as the expected value of the linear complexity of N-periodic sequences. Cryptographically strong sequences should not only have a large linear complexity, but also the change of a few terms should not cause a significant decrease of the linear complexity. This requirement leads to the concept of the k-error linear complexity LNk(S) of sequences S with period length N. For some k and c we determine the number of periodic sequences S with given period length N and LNk(S)=c. For prime N we establish a lower bound on the expected value of the k-error linear complexity.

Keywords

periodic sequences
linear complexity
k-error linear complexity
discrete Fourier transform

Cited by (0)

Research partially supported by the Austrian Science Fund (FWF) under Project S8306-MAT.

f1

E-mail: [email protected]

f2

E-mail: [email protected]