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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 Z 4 -code. As a consequence, it is shown that there are at least 94356 inequivalent extremal Type II Z 4 -codes of length 40 .
The purpose of this paper is to investigate the finite group which appears in the study of the Type II Z 4 -codes. To be precise, it is characterized in terms of generators and relations, and we determine the structure of the centralizer algebras of the tensor representations of this group.
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