The 4-error linear complexity distribution for $2^n$-periodic binary sequences
This work addresses a theoretical problem in cryptography and coding theory by providing exact distributions for error resilience in sequence complexity, but it is incremental as it extends prior methods to specific cases.
The paper tackles the problem of analyzing the k-error linear complexity distribution for 2^n-periodic binary sequences, specifically presenting complete counting functions for k=4 and 5 for balanced sequences and deriving results for 4-error complexity across all such sequences.
By using the sieve method of combinatorics, we study $k$-error linear complexity distribution of $2^n$-periodic binary sequences based on Games-Chan algorithm. For $k=4,5$, the complete counting functions on the $k$-error linear complexity of $2^n$-periodic balanced binary sequences (with linear complexity less than $2^n$) are presented. As a consequence of the result, the complete counting functions on the 4-error linear complexity of $2^n$-periodic binary sequences (with linear complexity $2^n$ or less than $2^n$) are obvious. Generally, the complete counting functions on the $k$-error linear complexity of $2^n$-periodic binary sequences can be obtained with a similar approach.