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A successor rule framework for constructing k-ary de Bruijn sequences and universal cycles
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2020-01-01 , DOI: 10.1109/tit.2019.2928292
D. Gabric , J. Sawada , A. Williams , D. Wong

We present a simple framework for constructing $k$ -ary de Bruijn sequences, and more generally, universal cycles, via successor rules. The framework is based on the often used method of joining disjoint cycles. It generalizes several previously known de Bruijn sequence constructions based on the pure cycling register and is applied to derive a new construction that is perhaps the simplest of all successors. Furthermore, it generalizes an algorithm to construct binary de Bruijn sequences based on any arbitrary nonsingular feedback function. The framework is applied to derive and prove the correctness of successors to efficiently construct 1) universal cycles for $k$ -ary strings of length $n$ whose weight is bounded by some $w$ and 2) universal cycles for permutations. It has also been subsequently applied to find the first universal cycle constructions for weak orders.

中文翻译:

用于构建 k-ary de Bruijn 序列和通用循环的后继规则框架

我们提出了一个简单的构建框架 $千$ -ary de Bruijn 序列,更一般地,通用循环,通过后继规则。该框架基于经常使用的连接不相交循环的方法。它概括了几个先前已知的基于纯循环寄存器的 de Bruijn 序列构造,并应用于推导可能是所有后继序列中最简单的新构造。此外,它概括了一种基于任意非奇异反馈函数构造二进制 de Bruijn 序列的算法。该框架用于推导和证明后继者的正确性,以有效地构建 1) 通用循环 $千$ -ary 长度的字符串 $n$ 其重量受某些限制 $w$ 和 2) 排列的通用循环。它随后也被用于寻找弱阶的第一个通用循环结构。
更新日期:2020-01-01
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