Orientable sequences over non-binary alphabets

TL;DR

This paper introduces recursive methods for constructing orientable sequences over any finite alphabet, generalizing binary cases, and provides an upper bound on their period, advancing sequence design theory.

Contribution

It presents new recursive construction techniques for orientable sequences over non-binary alphabets using generalized Lempel homomorphisms, extending previous binary-focused work.

Findings

Recursive construction methods for non-binary orientable sequences

Use of generalized Lempel homomorphisms in sequence construction

Derived an upper bound on the sequence period

Abstract

We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either direction. In particular we establish how two variants of a generalised Lempel homomorphism can be used to recursively construct such sequences, generalising previous work on the binary case. We also derive an upper bound on the period of an orientable sequence.