The 4-Variance Linear Complexity Distribution with 2n-Periodical Binary Sequences

Abstract

In this paper, the method of calculating the k-variance linear complexity distribution with 2n-periodical sequences by the Games-Chan algorithm and sieve approach is affirmed for its generality. The main idea of this method is to decompose a binary sequence into some subsequences of critical requirements, hence the issue to find k-variance linear complexity distribution with 2n-periodical sequences becomes a combinatorial problem of these binary subsequences. As a result, we compute the whole calculating formulas on the k-variance linear complexity with 2n-periodical sequences of linear complexity less than 2n for k = 4, 5. With combination of results in the whole calculating formulas on the 3-variance linear complexity with 2n-periodical binary sequences of linear complexity 2n, we completely solve the problem of the calculating function distributions of 4-variance linear complexity with 2n-periodical sequences elegantly, which significantly improves the results in the relating references.