Summary
the 2014 International Symposium on Nonlinear Theory and its Applications
2014
Session Number:D1L-C
Session:
Number:D1L-C1
An algorithm for generating all CR sequences in the de Bruijn sequences of length 2n where n is any odd number
Hiroshi Fujisaki,
pp.680-683
Publication Date:2014/9/14
Online ISSN:2188-5079
Summary:
For the case that p is any prime number, we have already constructed all CR (complement reverse) sequences in the de Bruijn sequences of length 2 2p+1. With the help of the Dyck language, we characterize CR sequences in the de Bruijn sequences of length 2 2m+1 where m(? 4) is a non-prime number. Then, we show that for any odd number n, there exist CR sequences in the de Bruijn sequences of length 2 n, which completely settles the fun- damental problem posed by Fredricksen on existence of the CR sequences. Consequently, we establish an algorithm for generating all CR sequences in the de Bruijn sequences of length 2 n for any odd n.