Article
Some necessary conditions for feedback functions of de Bruijn sequences
Authors
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Abstract
De Bruijn sequence is an important kind of nonlinear shift register sequence, which has a very wide range of applications in the fields of communication and cryptography. From the perspective of the relationship between linear terms, quadratic terms and cubic terms in the feedback functions of de Bruijn sequences, some new necessary conditions for feedback functions of de Bruijn sequences are obtained. Some examples show that the known necessary conditions cannot deduce the proposed necessary conditions.
Keywords
linear feedback shift register, nonlinear feedback shift register, de Bruijn sequence, feedback function, Boolean function, algebraic normal form, nonlinear term, 05A05, 11T06, 11T55
Citation
Hu, D., Chen, S., Xu, X., & Xiong, Y. (2021). Some necessary conditions for feedback functions of de bruijn sequences. Applied Mathematics and Nonlinear Sciences, 6(2), 215–224. https://doi.org/10.2478/amns.2021.2.00305
D. Hu, S. Chen, X. Xu and Y. Xiong, “Some necessary conditions for feedback functions of de bruijn sequences,” Applied Mathematics and Nonlinear Sciences, vol. 6, no. 2, pp. 215–224, 2021, doi: 10.2478/amns.2021.2.00305.
Hu D, Chen S, Xu X, Xiong Y. Some necessary conditions for feedback functions of de bruijn sequences. Applied Mathematics and Nonlinear Sciences. 2021;6(2):215–224. doi:10.2478/amns.2021.2.00305.
Hu, D., Chen, S., Xu, X. and Xiong, Y. (2021), ‘Some necessary conditions for feedback functions of de bruijn sequences’, Applied Mathematics and Nonlinear Sciences, 6(2), pp. 215–224. Available at: https://doi.org/10.2478/amns.2021.2.00305.
Hu, Daohuan, et al. “Some Necessary Conditions for Feedback Functions of De Bruijn Sequences.” Applied Mathematics and Nonlinear Sciences, vol. 6, no. 2, 2021, pp. 215–224. https://doi.org/10.2478/amns.2021.2.00305.
Hu, Daohuan, Shiqi Chen, Xiaofang Xu, and Yazhou Xiong. “Some Necessary Conditions for Feedback Functions of De Bruijn Sequences.” Applied Mathematics and Nonlinear Sciences 6, no. 2 (2021): 215–224. https://doi.org/10.2478/amns.2021.2.00305.
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Published by: Engineering Journals
