Orientable and negative orientable sequences
For researchers in automatic position-location applications, this work provides practical construction methods for orientable sequences over non-binary alphabets, achieving near-optimal periods.
This paper presents three techniques for generating negative orientable sequences over arbitrary finite alphabets and establishes upper bounds on their period. Using these sequences, the authors construct orientable sequences with period close to the maximum possible for every non-binary alphabet size and tuple length.
Analogously to de Bruijn sequences, orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., a range of methods of construction were described for orientable sequences over arbitrary finite alphabets; some of these methods involve using negative orientable sequences as a building block. In this paper we describe three techniques for generating such negative orientable sequences, as well as upper bounds on their period. We then go on to show how these negative orientable sequences can be used to generate orientable sequences with period close to the maximum possible for every non-binary alphabet size and for every tuple length. In doing so we use two closely related approaches described by Alhakim et al.