Joint linear complexity of arbitrary multisequences consisting of linear recurring sequences


Fu F., Niederreiter H., ÖZBUDAK F.

FINITE FIELDS AND THEIR APPLICATIONS, vol.15, no.4, pp.475-496, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 4
  • Publication Date: 2009
  • Doi Number: 10.1016/j.ffa.2009.03.001
  • Title of Journal : FINITE FIELDS AND THEIR APPLICATIONS
  • Page Numbers: pp.475-496

Abstract

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.