On the existence of extremal Type II ℤ_{2𝕜}-codes

Harada, Masaaki; Miezaki, Tsuyoshi

doi:10.1090/S0025-5718-2013-02750-0

On the existence of extremal Type II $\mathbb {Z}_{2k}$-codes
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Math. Comp. 83 (2014), 1427-1446 Request permission

Abstract:

For lengths $8$, $16$, and $24$, it is known that there is an extremal Type II $\mathbb {Z}_{2k}$-code for every positive integer $k$. In this paper, we show that there is an extremal Type II $\mathbb {Z}_{2k}$-code of lengths $32,40,48,56$, and $64$ for every positive integer $k$. For length $72$, it is also shown that there is an extremal Type II $\mathbb {Z}_{4k}$-code for every positive integer $k$ with $k \ge 2$.

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