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

Masaaki Harada

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 $40$.

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