On optimal constant weight codes derived from $\omega$-circulant balanced generalized weighing matrices

TL;DR

This paper constructs optimal constant weight codes using a new family of $ircirculant balanced weighing matrices, enhancing coding theory with explicit algebraic structures for specific parameters.

Contribution

It introduces a novel family of $ircirculant balanced weighing matrices and demonstrates their application in constructing optimal constant weight codes.

Findings

Codes are optimal for specified parameters.

Explicit algebraic construction of matrices.

Improved bounds for code parameters.

Abstract

A family of $\omega$-circulant balanced weighing matrices with classical parameters is used for the construction of optimal constant weight codes over an alphabet of size $g+1$ and length $n=(q^m -1)/(q-1)$, where $q$ is an odd prime power, $m>1$, and $g$ is a divisor of $q-1$.