De Bruijn sequences with efficient decoding algorithms Original Research Article

A de Bruijn sequence of span n is a periodic sequence in which every n-tuple over the alphabet appears exactly once, starting within the minimal generating cycle of the sequence. The decoding problem for such a sequence is to determine the position of an arbitrary n-tuple over the alphabet. Algorithms that allow this problem to be solved efficiently are important in certain types of position sensing applications. We present constructions for de Bruijn sequences over a variety of alphabets, together with corresponding decoding algorithms, that constitute a significant improvement over existing methods. These results include a construction for binary de Bruijn sequences of arbitrary span whose decoding algorithm is both fast and storage-free.