On a class of optimal constant weight ternary codes

TL;DR

This paper constructs a class of optimal constant weight ternary codes using weighing matrices, providing explicit parameters and demonstrating their optimality for certain prime powers and integers.

Contribution

It introduces a novel construction of optimal constant weight ternary codes via weighing matrices for specific parameters.

Findings

Constructed weighing matrices of order n with specified weights.

Rows of these matrices form optimal ternary codes with given parameters.

Established the exact maximum size of these codes for the parameters.

Abstract

A weighing matrix $W$ of order $n=\frac{p^{m+1}-1}{p-1}$ and weight $p^m$ is constructed and shown that the rows of $W$ and $-W$ form optimal constant weight ternary codes of length $n$, weight $p^m$ and minimum distance $p^{m-1}(\frac{p+3}{2})$ for each odd prime power $p$ and integer $m\ge 1$ and thus $$A_3\left(\frac{p^{m+1}-1}{p-1},p^{m-1}\big(\frac{p+3}{2}\big),p^{m}\right)=2\big(\frac{p^{m+1}-1}{p-1}\big).$$