Enumeration results on the joint linear complexity of multisequences

Recent developments in stream ciphers point towards an interest in word-based or vectorized stream ciphers. Such stream ciphers suggest the study of the joint linear complexity of multisequences. In this paper, using the first author's multisequence linear feedback shift-register synthesis algorithm based on a lattice basis reduction algorithm in function fields, we present a method to determine the value of , the number of m-fold multisequences of length n over a finite field Fq with nth joint linear complexity L. Furthermore, a closed-form expression for and formulas for the expected value of the joint linear complexity and its variance are given when m=2.