Investigating the discrepancy property of de Bruijn sequences

05/04/2020 ∙ by Daniel Gabric, et al. ∙ 0

The discrepancy of a binary string refers to the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. We provide an investigation of the discrepancy of known simple constructions of de Bruijn sequences. Furthermore, we demonstrate constructions that attain the lower bound of Θ(n) and a new construction that attains the previously known upper bound of Θ(2^n/√(n)). This extends the work of Cooper and Heitsch [Discrete Mathematics, 310 (2010)].

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 5

page 10

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.