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In this paper, we determine the dimensions of the residue codes of extremalType II Z4-codes for lengths 32 and 40. We demonstrate that every binary doublyeven self-dual code of length 32 can be realized as the residue code of someextremal Type II Z4-code. It is also shown that there is a unique extremal TypeII Z4-code of length 32 whose residue code has the smallest dimension 6 up toequivalence. As a consequence, many new extremal Type II Z4-codes of lengths 32and 40 are constructed.

On the Residue Codes of Extremal Type II Z4-Codes of Lengths 32 and 40