Constructing orientable and negative orientable sequences with asymptotically optimal period

TL;DR

This paper introduces a new method for constructing orientable and negative orientable sequences with asymptotically optimal periods, improving sequence design for position location applications.

Contribution

It extends existing approaches to generate negative orientable sequences with more $n$-tuples, achieving asymptotically optimal periods and enabling improved orientable sequence construction.

Findings

Sequences with asymptotically optimal period constructed

Enhanced method for negative orientable sequences

Sequences applicable to position location applications

Abstract

Orientable sequences, periodic sequences in which any $n$-tuple appears at most once in either direction, were introduced in the early 1990s for use in certain position location applications; constructions and upper bounds on the period for the binary case were published by Dai et al. More recent work has focussed on $k$-ary sequences for arbitrary $k>2$; one method of construction involves negative orientable sequences, in which an $n$-tuple appears at most once in either the sequence or the negative of its reverse. In this paper we show how additional $n$-tuples can be added to one previously described approach for generating negative orientable sequences, resulting in new sequences with asymptotically optimal period. These sequences can in turn be used to generate orientable sequences, again with asymptotically optimal period.