论文标题
一种确定二元修改的de bruijn序列的最小多项式的新方法
A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences
论文作者
论文摘要
二进制修饰的de bruijn序列是通过从二元de bruijn序列中最长的零运行中删除零的零来得出的无限二进制序列。修改序列的最小多项式是其独特的最低度特征多项式。利用最近的特征，我们设计了一种新型的通用方法来确定最小的多项式。我们将表征转换为在特殊构造的图中识别哈密顿周期的问题。一路上，我们在修改后的设置中演示了从周期加入方法中计算工具的有用性。
A binary modified de Bruijn sequence is an infinite and periodic binary sequence derived by removing a zero from the longest run of zeros in a binary de Bruijn sequence. The minimal polynomial of the modified sequence is its unique least-degree characteristic polynomial. Leveraging on a recent characterization, we devise a novel general approach to determine the minimal polynomial. We translate the characterization into a problem of identifying a Hamiltonian cycle in a specially constructed graph. Along the way, we demonstrate the usefullness of computational tools from the cycle joining method in the modified setup.
