Linear Difference Equations and Periodic Sequences over Finite Fields

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• 作者：Dang Vu Giang
• 关键词：Jordan multiplicative decomposition ; Characteristic equations ; Lucas’ congruence ; Minimal polynomial ; Trace representation ; Max ; sequences ; 12E20 ; 12Y05
• 刊名：Acta Mathematica Vietnamica
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：41
• 期：1
• 页码：171-181
• 全文大小：225 KB
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• 作者单位：Dang Vu Giang (1)
  
  1. Hanoi Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307, Hanoi, Vietnam
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Singapore
• ISSN：2315-4144

文摘

First, we study linear equations over finite fields in general. An explicit formula for a common period is found for every solution of a linear difference equation over a finite field. It will help to estimate the p-adic modulus of polynomial roots. Second, we focus our attention on periodic sequences over finite fields and Hamiltonian cycles in de Bruijn directed graph. Keywords Jordan multiplicative decomposition Characteristic equations Lucas’ congruence Minimal polynomial Trace representation Max-sequences