On Characteristic Functions of De Bruijn Sequences

TANG Zhenwei; QI Wenfeng; TIAN Tian

doi:10.1049/cje.2016.03.017

TANG Zhenwei, QI Wenfeng, TIAN Tian. On Characteristic Functions of De Bruijn Sequences[J]. Chinese Journal of Electronics, 2016, 25(2): 304-311. DOI: 10.1049/cje.2016.03.017

Citation:

TANG Zhenwei, QI Wenfeng, TIAN Tian. On Characteristic Functions of De Bruijn Sequences[J]. Chinese Journal of Electronics, 2016, 25(2): 304-311. DOI: 10.1049/cje.2016.03.017

Citation:

TANG Zhenwei, QI Wenfeng, TIAN Tian. On Characteristic Functions of De Bruijn Sequences[J]. Chinese Journal of Electronics, 2016, 25(2): 304-311. DOI: 10.1049/cje.2016.03.017

On Characteristic Functions of De Bruijn Sequences

Graphical Abstract

Graphical Abstract

Abstract

Abstract

In 1982, H. Fredricksen presented the upper and lower bounds of the number of ones in the truth table of characteristic functions of de Bruijn sequences. In this paper, the distribution of ones in the truth table of characteristic functions of de Bruijn sequences is further studied. We provide the upper and lower bounds of the number of ones in the partial truth table of characteristic functions of de Bruijn sequences. Furthermore, the two bounds are tight.