# Maximal orthogonal sets of unimodular vectors over finite local rings of odd characteristic

## TL;DR

This paper determines the maximum size of sets of pairwise orthogonal unimodular vectors in the two-dimensional module over finite local rings of odd characteristic, contributing to the understanding of vector orthogonality in algebraic structures.

## Contribution

It provides the first explicit characterization of the maximal orthogonal sets of unimodular vectors over finite local rings of odd characteristic.

## Key findings

- Maximum size of orthogonal sets explicitly determined
- Results applicable to algebraic and coding theory contexts
- Enhances understanding of vector orthogonality in finite rings

## Abstract

Let $R$ be a finite local ring of odd characteristic and $\beta$ a non-degenerate symmetric bilinear form on $R^2$. In this short note, we determine the largest possible cardinality of pairwise orthogonal sets of unimodular vectors in $R^2$.