Extremal Type II ${\mathbb{Z}}_4$-codes constructed from binary doubly even self-dual codes of length $40$

Abstract

In this note, we demonstrate that every binary doubly even self-dual code of length $40$ can be realized as the residue code of some extremal Type II ${\mathbb{Z}}_4$-code. As a consequence, it is shown that there are at least $94356$ inequivalent extremal Type II ${\mathbb{Z}}_4$-codes of length $40$.

6 pages