The Canonical Factorization of the Polynomial x~n-1 on F_q
Xuhong Li · Journal of Shanghai Second Polytechnic University · 2009
The linear complexity of sequences is one of the important security measures for stream cipher systems.Recently,in the study of vectored stream cipher systems,the joint linear complexity of multi-sequences has been investigated.In this paper,the algorithm of simples s=oq(n) is given.By this result,the author studies the canonical factorization of x n-1on Fq,and obtains the number of all monic polynomials with same degrees for the canonical factorization of x n-1on Fq using Inclusion-Exclusion Principle.These results are the foundation for counting of the joint linear complexity of multi-sequences withal expectation and variance.