Constructing Orientable Sequences

This paper describes new, simple, recursive methods of construction for orientable sequences, i.e. periodic binary sequences in which any $n$ -tuple occurs at most once a period either direction. As has been previously described, such have potential applications automatic position-location systems, where the sequence is encoded onto surface and reader needs only examine consecutive bits to determine its location orientation on surface. The described method (due Dai et al.) somewhat complex, whereas new techniques are simple both describe implement. cover standard ‘infinite periodic’ case, also aperiodic, finite sequence, case. Both build Lempel homomorphism, first introduced as means recursively generating de Bruijn sequences.