Primitive polynomials and word oriented linear feedback shift registers

ZENG Guang; YANG Yang; HAN Wen-bao; FAN Shu-qin

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Primitive polynomials and word oriented linear feedback shift registers

更新时间：2024-10-14

- Primitive polynomials and word oriented linear feedback shift registers
- Vol. 30, Issue S2, Pages: 111-116(2009)
- 作者机构：
  
  解放军信息工程大学
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN918.1
- Published：2009
- 稿件说明：
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ZENG Guang, YANG Yang, HAN Wen-bao, et al. Primitive polynomials and word oriented linear feedback shift registers[J]. 2009, 30(S2): 111-116.
DOI：

ZENG Guang, YANG Yang, HAN Wen-bao, et al. Primitive polynomials and word oriented linear feedback shift registers[J]. 2009, 30(S2): 111-116. DOI：

摘要

通过大量实验数据提出了有限域上本原σ-线性反馈移位寄存器(σ-LFSR)的个数猜想

利用给出的3种本原σ-LFSR的判别方法

证明了该猜想在3种情况下的正确性。该猜想是有限域上本原LFSR个数的推广

同时也是有限域上本原多项式的计数推广

为寻找本原σ-LFSR奠定了基础。

Abstract

Through a large number of experiments

an explicit formula was proposed for the number of primitive σ-LFSRs over finite field

which generalized a known formula for the number of primitive LFSRs over finite field

and also was the extension of the number of primitive polynomial.Utilizing the given methods to distinguish the primitive σ-LFSR

the conjecture in three special cases was proved and a preliminary analysis for the general case was given.

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Related Institution

Key Laboratory of Computer Networks and Information Security,Ministry of Education School of Computer Science＆Technology,Xidian University

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State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications

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Faculty of Mathematical Sciences, Luoyang Normal University

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