The Tight Error Linear Complexity of Periodic Sequences

Abstract

Based on linear complexity, k-error linear linear complexity, k-error linear complexity profile and minerror, the m-tight error linear complexity is presented to study the stability of the linear complexity of periodic sequences. The m-tight error linear complexity of sequence S is defined as a two tuple (km, LCm), which is the mth jump point of the k-error linear complexity profile of sequence S. The Wei-Xiao-Chen algorithm can not be generalized into a k-error linear linear complexity algorithm as it does not have a Stamp-Martin pattern. By using error vectors, an efficient approach for computing m-tight error linear complexity of binary sequences with period 2 n p m is given. One of our main contributions is to show that every fast algorithm for linear complexity can be generalized to a fast algorithm for m-tight error linear complexity for small m.

Research on Excellent p^n-periodic Binary Sequence with Genetic Algorithm

“…In [5], Zhou et al introduced the algorithm for determining m-tight linear complexity of binary sequence with period ‫‬ . The m-tight linear complexity of sequence S is a two tuple (݇ , ‫ܥܮ‬ ), which is the m-th jump point of the k-error linear complexity profile of sequence S. Each run the algorithm with input ݇ will give an output ‫ܥܮ‬ and a number ܶ min , which is the value of ݇ ାଵ that the (݇ ାଵ − 1)-error linear complexity is equal to ‫ܥܮ‬ and the ݇ ାଵ -error linear complexity is less than ‫ܥܮ‬ .…”

“…In [5] and [6], Zhou et al introduced the m-tight linear complexity. The m-tight linear complexity of sequence S is defined as a two tuple (݇ , ‫ܥܮ‬ ), which is the m-th jump point of the k-error linear complexity profile of sequence S. They also introduced a k-error linear complexity algorithm for a binary sequence with period ‫‬ , in which the computation of the cost is different from that in Stamp-Martin algorithm.…”