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The Minimal Polynomial over F_q of Linear Recurring Sequence over F_{q^m}
- Publication Year :
- 2009
-
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}.<br />Comment: Submitted to the journal Finite Fields and Their Applications
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.0904.0525
- Document Type :
- Working Paper