确定二元修正de Bruijn序列极小多项式的一种新方法
A New Approach to Determine the Minimal Polynomials of Binary Modified de Bruijn Sequences
摘要：
二进制修正德布鲁因序列（英语：Binary modified de Bruijn sequence）是一个无限长的周期性二进制序列，它是通过从二进制德布鲁因序列中最长的零行程中删除一个零而得到的。修正序列的最小多项式是其唯一的最小次数特征多项式。利用最近的表征，我们设计了一种新的一般方法来确定最小多项式。我们翻译成一个问题，确定一个特殊构造的图中的哈密尔顿循环的表征。一路上，我们证明了有用的计算工具，从循环加入方法在修改后的设置。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
