New self-dual codes over GF(4) with the highest known minimum weights

The purpose of this correspondence is to construct new Hermitian self-dual codes over GF(4) of lengths 22, 24, 26, 32, and 34 which have the highest known minimum weights. In particular, for length 22, we construct eight new extremal self-dual [22,11,8] codes over GF(4) which do not have a nontrivial automorphism of odd order. The existence of such codes has been left open since 1991 by Huffman.