Joint linear complexity of arbitrary multisequences consisting of linear recurring sequences

Let g1,…,gs∈Fq[x] be arbitrary nonconstant monic polynomials. Let M(g1,…,gs) denote the set of s-fold multisequences (σ1,…,σs) such that σi is a linear recurring sequence over Fq with characteristic polynomial gi for each 1⩽i⩽s. Recently, we obtained in some special cases (for instance when g1,…,gs are pairwise coprime or when g1=⋯=gs) the expectation and the variance of the joint linear complexity of random multisequences that are uniformly distributed over M(g1,…,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(g1,…,gs) in the general case.