  A timing and synchronization system based on a de Bruijn sequence has been
proposed and studied recently for a channel associated with quantum
communication that requires reliable synchronization. To avoid a long period of
no-pulse in such a system on-off pulses are used to simulate a zero and on-on
pulses are used to simulate a one. However, these sequences have high
redundancy. To reduce the redundancy, run-length limited sequences in the de
Bruijn graph are proposed for the same purpose. The maximum length of such
sequences in the de Bruijn graph is studied and an efficient algorithm to
construct a large set of these sequences is presented. A maximum length
sequence for which the position of each window can be computed efficiently is
constructed. Finally, an enumeration of the number of such sequences is given
and some generalizations are discussed.
