Joint linear complexity of arbitrary multisequences consisting of linear recurring sequences

Let g(1),..., g(s) is an element of F-q[x] be arbitrary nonconstant monic polynomials. Let M(g(1),..., g(s)) denote the set of s-fold multisequences (sigma(1),...,sigma(s)) such that sigma(i) is a linear recurring sequence over F-q with characteristic polynomial g(i) for each 1 <= i <= s. Recently, we obtained in some special cases (for instance when gl,..., gs are pairwise coprime or when g(1) = ... = g(s)) the expectation and the variance of the joint linear complexity of random multisequences that are uniformly distributed over M(g(1),..., gs). However, the general case seems to be much more complicated. In this-paper we determine the expectation and the variance of the joint linear complexity of random multisequences that are uniformly distributed over M(g(1),..., g(s)) in the general case. (C) 2009 Elsevier Inc. All rights reserved.