A classification of all four-circulant extremal codes of length 32 over F2 +
uF2 is done by using four-circulant binary self-dual codes of length 32 of
minimum weights 6 and 8. As Gray images of these codes, a substantial number
of extremal binary self-dual codes of length 64 are obtained. In particular a
new code with ?=80 in W64,2 is found. Then applying an extension method from
the literature to extremal self-dual codes of length 64, we have found many
extremal binary self-dual codes of length 66. Among those, five of them are
new codes in the sense that codes with these weight enumerators are
constructed for the first time. These codes have the values ?=1, 30, 34,
84, 94 in W66,1.
On the Hamming Weight Enumerators of Self-Dual Codes over Zk
