In this note, an extremal doubly-even [40, 20, 8] code with covering radius 7 is given. This code is the first extremal doubly-even code whose covering radius does not meet the Delsarte bound. Extremal singly-even codes with the smallest covering radius are also given. One of them is an extremal singly-even [44, 22, 8] code with covering radius 7, which determines t[43, 22] = 6 by puncturing.
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