On the self-dual codes invariant under an automorphism of type 11-(8,0)

We study self-dual codes (SD) over GF(2) with 8 cycles of length 11 in the decomposition of its automorphism and minimum weight at least 16. The main method we use is by Huffman and Yorgov and is for constructing SD codes having an automorphism of order p for a prime p > 2. We prove that [8],[4] SD codes over F210 such that their preimage is a binary code with minimum weight 20 does not exist. By restricting the matrices of the subcode to have symmetric or circulant submatrix in their systematic form, we have found many new Hermitian self-dual codes over F210. Those newly found Hermitian codes allow us to constructed 468062 new binary SD [88,44,16] doubly-even codes.