MSc Seminar: Daniel Gabric

TITLE: 

De Bruijn sequence constructions based on concatenation schemes​

ABSTRACT:
A universal cycle for a set S is a circular sequence that contains every element of S as a substring exactly once. A binary de Bruijn sequence of order n is a universal cycle where S is the set of all binary strings. A co-necklace is the lexicographically smallest string in an equivalence class of strings under the complemented cycling register. We present a new de Bruijn sequence construction based on concatenating co-necklaces in colexicographic order, and a general method for concatenating universal cycles. We also show that the discrepancy of a concatenation scheme from co-necklaces is bounded above by 2n.

Advisor:  Dr. Joseph Sawada

Advisory Committee Member: Dr. David Calvert