F_{q^m}上线性递归序列的F_q上的极小多项式
The Minimal Polynomial over F_q of Linear Recurring Sequence over F_{q^m}
摘要：
近年来，受向量化流密码系统研究的启发，多序列的联合线性复杂度和联合最小多项式得到了研究。设S是有限域F_{q^m}上的线性递归序列，其最小多项式h（x）是F_{q^m}上的.由于F_{q^m}和F_{q} ^m是有限域F_q上的同构向量空间，S被有限域F_q上的m重序列S^{（m）}所标识. m重序列S^{（m）}的联合最小多项式和联合线性复杂度分别是S在F_q上的最小多项式和线性复杂度。本文研究了F_{q^m}上线性递归序列S在F_q上的极小多项式和线性复杂度，其中h（x）是F_{q^m}上的极小多项式.如果h（x）在F_{q^m} [x]中的标准分解已知，则我们确定了F_{q^m}上线性递归序列S在F_q上的最小多项式和线性复杂度.
英文摘要：
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}.
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