Research On K-Error Linear Complexity Of Periodic Binary Sequences

The security of information becomes more and more important along with Information Times arrives.How to encrypt or decipher, becomes a topic of general which is researched by many scholars and experts.Therefore,linear complexity and k-error linear complexity which are indexs of cryptograph security,receive more and more attention.The main idea of it is studying on how to use the least levels of FCSR to obtain the sequence which we expect or the sequence similar to which we expect.It can be found that linear complexity and k-error linear complexity are very important in judging the security of sequence cipher,by researching on sequences of various feild or various period.Because cryptograph are usually binary sequences,it is more important to study on linear complexity and k-error linear complexity of periodic binary sequences.In order to describe k-error linear complexity of periodic binary sequences exactly, we give a more exact bound on expected value of k-error linear complexity of periodic binary sequencescalculate the expected values of 2-error and 3-error linear complexity of periodic binary sequences ( E₂,E₃) and k-error linear complexity of distinct sequences, and we also calculate the jump-points of k-error linear complexity of some specialperiodic binary sequences which are equal to k_i =W(sum from e=m to i+m (1+x)^2e-1), and k_i-error linear complexity LC_ki (S)=2ⁿ-2^(m+l)+i+1 (0≤i≤M-m) .