TL;DR
This paper investigates bounds on dot product configurations over Galois rings, addressing a problem related to the Erdős Unit Distance Conjecture, and also establishes bounds for an inverse vector matrix multiplication problem.
Contribution
It introduces new bounds for dot product configurations in Galois rings and provides results on inverse vector matrix multiplication problems.
Findings
Bound on dot product configurations over Galois rings
Bound on inverse vector matrix multiplication
Insights related to Erdős Unit Distance Conjecture
Abstract
We consider a problem related to the Erdo\H{o}s Unit Distance Conjecture: How often can a single dot product configuration or a multiple dot product configuration occur over a Galoi Ring? We also find a bound on an inverse vector matrix multiplication problem.
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Taxonomy
TopicsCoding theory and cryptography · Polynomial and algebraic computation · Commutative Algebra and Its Applications