On the error linear complexity profiles of binary sequences of period 2n

This paper studies the error linear complexity profiles of binary sequences with period 2
ⁿ
. We give a precise categorization of those sequences having 2 distinct critical points in their profiles, as well as an enumeration of these sequences. We also give an upper bound on the maximum number of distinct critical points that the profile of a sequence can have, along with several constructions for sequences having many distinct critical points.