The minimal polynomial over [formula omitted] of linear recurring sequence over [formula omitted

Abstract

Recently, motivated by the study of vectorized stream cipher systems, the joint linear complexity and joint minimal polynomial of multisequences have been investigated. Let S be a linear recurring sequence over finite field F q m with minimal polynomial h ( x ) over F q m . Since F q m and F q m are isomorphic vector spaces over the finite field F q , S is identified with an m-fold multisequence S ( m ) over the finite field F q . The joint minimal polynomial and joint linear complexity of the m-fold multisequence S ( m ) are the minimal polynomial and linear complexity over F q of S , respectively. In this paper, we study the minimal polynomial and linear complexity over F q of a linear recurring sequence S over F q m with minimal polynomial h ( x ) over F q m . If the canonical factorization of h ( x ) in F q m [ x ] is known, we determine the minimal polynomial and linear complexity over F q of the linear recurring sequence S over F q m .