On the $[24,12,8]$ Self-Dual Quaternary Codes

Abstract

We construct all self-dual $[24,12,8]$ quaternary codes with a monomial automorphism of prime order $r>3$ and obtain a unique code for $r=23$ (which has automorphisms of orders $5$, $7$, and $11$ too), two inequivalent codes for $r=11$, $6$ inequivalent codes for $r=7$, and $12$ inequivalent codes for $r=5$. The obtained codes have $12$ different weight spectra.