On Stability Of The Linear Complexity For Periodic Sequences

The linear complexity of keystreams is an important measure index of stream ciphers,but for some sequences their linear complexity are not stable,that is after change one or some bits cause a significant change of their complexity.Aim at this problem,our domestic scholar founded the stability theory for stream ciphers,and introduced the notion such as sphere complexity and weight complexity,which are the measure index of the stability of stream ciphers.Foreign scholar also intro-duced the notion of k-error linear complexity which our domestic scholar called sphere complexity, thereby k-error linear complexity reflect the stability of the linear complexity of sequences very well from some profile.But the gained research of the k-error linear complexity only gained the bounds of some measure indexes.So for some idiographic keystreams how to improve these bounds is very important.The representation of sequences is very helpful for the research of their linear complexity,so this paper we first research trace representation of periodic sequences,and the trace representation of a New Generalized Cyclotomic Sequence of order two of length pq is given,then for 2~mp~n period binary sequences,where p is an odd prime and 2 is a primitive root modulo p~2,we present a relation-ship between the linear complexity and the minimum value k for which the k-error linear complexity is strictly less than the linear complexity and have the upper bound and lower bound of the value k, finally we discuss the k-error linear complexity of legendre sequences,also have the upper bound and lower bound of the value k,and discusses the situation where the linear complexity drop again for some Legendre sequences.