On prefer-one sequences

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-10 DOI:10.1007/s10623-024-01425-7

Yupeng Jiang, Ming Li, Ying Gao, Dongdai Lin

引用次数: 0

Abstract

We study the sequences generated by prefer-one rule with different initial vectors. Firstly, we give upper bounds of their periods and for initial vectors with Hamming weight one, we prove that the generated sequences are modified de Bruijn sequences. Moreover, for two of them, we give the truth tables of their feedback functions. We also investigate the feedback functions of prefer-one de Bruijn sequences. For order n prefer-one de Bruijn sequence, we give linear and quadratic terms in its feedback function and prove that the number of degree \(n-2\) terms has the same parity as n. The statistical result for small n shows that about half of all terms occur in the feedback functions.

Abstract Image

查看原文本刊更多论文

关于优选序列

我们研究了用 prefer-one 规则生成的具有不同初始向量的序列。首先，我们给出了它们的周期上限，对于汉明权重为 1 的初始向量，我们证明了生成的序列是修正的德布鲁因序列。此外，我们还给出了其中两个序列的反馈函数真值表。我们还研究了优选一德布鲁因序列的反馈函数。对于 n 阶 prefer-one de Bruijn 序列，我们给出了其反馈函数中的线性项和二次项，并证明了度（n-2）项的数量与 n 具有相同的奇偶性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.