  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 in a period in either direction. As has been previously
described, such sequences have potential applications in automatic
position-location systems, where the sequence is encoded onto a surface and a
reader needs only examine n consecutive encoded bits to determine its location
and orientation on the surface. The only previously described method of
construction (due to Dai et al.) is somewhat complex, whereas the new
techniques are simple to both describe and implement. The methods of
construction cover both the standard `infinite periodic' case, and also the
aperiodic, finite sequence, case. Both the new methods build on the Lempel
homomorphism, first introduced as a means of recursively generating de Bruijn
sequences.
