LINEAR COMPLEXITY AND RELATED COMPLEXITY MEASURES
The linear complexity of a sequence is not only a measure for the unpredictability and thus suitability for cryptography but also of interest in information theory because of its close relation to the Kolmogorov complexity. However, in contrast to the Kolmogorov complexity the linear complexity is computable and so of practical significance.
It is also linked to coding theory. On the one hand, the linear complexity of a sequence can be estimated in terms of its correlation and there are strong ties between low correlation sequence design and the theory of error-correcting codes. On the other hand, the linear complexity can be calculated with the Berlekamp-Massey algorithm which was initially introduced for decoding BCH-codes.
This chapter surveys several mainly number theoretic methods for the theoretical analysis of the linear complexity and related complexity measures and describes several classes of particularly interesting sequences with high linear complexity.