2021/08/06 by Chris J. Mitchell, Mitchell, Chris J, Peter Wild +1 · 1 citation
Computer Science · #Algorithms and Data Compression #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · doi:10.48550/arxiv.2108.03069
openalex publication_date 2021/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.