On the k-Operation Linear Complexity of Periodic Sequences

Abstract

Non-trivial lower bounds on the linear complexity are derived for a sequence obtained by performing k or fewer operations on a single period of a periodic sequence over $\mathbb{F}_q$. An operation is a substitution, an insertion, or a deletion of a symbol. The bounds derived are similar to those previously established for either k substitutions, k insertions, or k deletions within a single period. The bounds are useful when T/2k < L < T/k, where L is the linear complexity of the original sequence and T is its period.