Perfect Sequences and Arrays over the Unit Quaternions
Sam Blake
TL;DR
This paper presents new constructions of perfect autocorrelation sequences and arrays over the unit quaternions, including odd-perfect sequences of unbounded lengths with good zero-correlation zones, supported by mathematical proofs and computer experiments.
Contribution
It introduces novel methods for constructing perfect quaternion sequences and arrays, expanding the possibilities for applications requiring ideal autocorrelation properties.
Findings
New constructions of perfect sequences and arrays over unit quaternions.
First sequence construction of odd-perfect sequences with unbounded lengths.
Validated perfect autocorrelation through proofs and computer experiments.
Abstract
We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have perfect periodic auto- correlation. Furthermore, the first sequence construction generates odd-perfect sequences of unbounded lengths, with good ZCZ.
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Taxonomy
TopicsAntenna Design and Optimization · Wireless Communication Networks Research · Cellular Automata and Applications