Construction of extremal Type II $\mathbb{Z}_{2k}$-codes

Abstract: We give methods for constructing many self-dual

m a t h b b Z_{m}

-codes and Type II

m a t h b b Z_{2 k}

-codes of length

2 n

starting from a given self-dual

m a t h b b Z_{m}

-code and Type II

m a t h b b Z_{2 k}

-code of length

2 n

, respectively. As an application, we construct extremal Type II

m a t h b b Z_{2 k}

-codes of length

24

for

k = 4, 5, l d o t s, 20

and extremal Type II

m a t h b b Z_{2 k}

-codes of length

32

for

k = 4, 5, l d o t s, 10

. We also construct new extremal Type II

m a t h b b Z_{4}

-codes of lengths

56

and

64

.

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