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

Balanced generalized weight matrices are used to construct optimal constant weight codes that are monomially inequivalent to codes derived from the classical simplex codes. What’s more, these codes can be assumed to be generated entirely by \(\omega \) $\omega$ -shifts of a single codeword where \(\omega \) $\omega$ is a primitive element of a Galois field. Additional constant weight codes are derived by projecting onto subgroups of the alphabet sets. These too are shown to be optimal.