Extremal self-dual [40, 20, 8] codes with covering radius 7

We construct new extremal self-dual [40,20,8] codes with covering radius 7. It is also shown that the vectors of a fixed weight in a coset of weight 4n+2 in an extremal doubly even self-dual code of length 24n+16 such that the coset has no vector of weight 4n+4 form a 1-design.

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