Linear complexity of transformed sequences

Abstract

This paper deals with the effect of bit change errors on the linear complexity of finite sequences. Though a change in a single bit can cause a large change in linear complexity, it is shown that on the average the change will be small even when many bits, e.g. 10%, are changed. General bijections on the set of sequences of length n are studied and tight bounds are found on the average difference in linear complexity between a sequence and its image. It is also shown that to change all sequences of length n into sequences with linear complexity less than c(n) where lim_n→∞ c(n)/n=0, at least n−1/n2ⁿ of the sequences must have close to half of their bits changed.

This work was supported in part by The Institut National de Recherche en Informatique et en Automatique, Rocquencourt, France.