论文标题
调查de bruijn序列的差异特性
Investigating the discrepancy property of de Bruijn sequences
论文作者
论文摘要
二进制字符串的差异是指在给定二进制字符串的所有可能子字上的零数量和零数之间的最大（绝对）差异。我们对De Bruijn序列的已知简单结构的差异进行了研究。此外，我们演示了达到$θ（n）$的下限的构造，并且新的结构是获得$θ（\ frac {2^n} {\ sqrt {n}}）$的先前已知上限的构造。这扩展了Cooper和Heitsch〜 [\ emph {iNCETE MATHEMATICS}，310（2010）]的工作。
The discrepancy of a binary string refers to the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. We provide an investigation of the discrepancy of known simple constructions of de Bruijn sequences. Furthermore, we demonstrate constructions that attain the lower bound of $Θ(n)$ and a new construction that attains the previously known upper bound of $Θ(\frac{2^n}{\sqrt{n}})$. This extends the work of Cooper and Heitsch~[\emph{Discrete Mathematics}, 310 (2010)].
