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Paper IDT.4.3
Paper Title The Numbers of De Bruijn Sequences in Extremal Weight Classes
Authors Ming Li, Yupeng Jiang, Dongdai Lin, State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, China
Session T.4: Sequences
Presentation Lecture
Track Topics in Information Theory
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract In this paper, we analyze the weight class distribution of de Bruijn sequences. The main tool we use is the generating function theory, proposed recently by Coppersmith et al. By analyzing the weights of cycles generated by the pure circulating register, we give explicit formulas for the numbers of de Bruijn sequences in the extremal weight classes. Moreover, we use these formulas to prove some conjectures proposed by Fredricksen and Mayhew, which seems have been opened for a long time. In addition to these theoretical results, some experimental results are also provided.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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