|The Numbers of De Bruijn Sequences in Extremal Weight Classes
|Ming Li, Yupeng Jiang, Dongdai Lin, State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, China
|Topics in Information Theory
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|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.