On some new extremal Type II Z4-codes of length 40

Abstract

Using the building-up method and a modification of the doubling method we construct new extremal Type II  Z4-codes of length 40. The constructed codes of type $4^{k_1}2^{k_2}$, for $\ k_1\in \{8,9,10,11,12,14,15\}$,
are the first examples of extremal Type II  Z4-codes of given type and length 40 whose residue codes have minimum weight greater than or equal to 8. Further, we use minimum weight codewords for a construction of 1-designs, some of which are self-orthogonal.