Partitioning de Bruijn graphs into fixed-length cycles for robot identification and tracking

We provide several existence results that give the maximum number of cycles in dB(q,ℓ) in various cases. For example, we give an optimal solution when k=qℓ−1. Another construction yields many cycles in larger de Bruijn graphs using cycles from smaller de Bruijn graphs: if dB(q,ℓ) can be partitioned into k-cycles, then dB(q,tℓ) can be partitioned into tk-cycles for any divisor t of k. The methods used are based on finite field algebra and the combinatorics of words.