On the Binary Self-complementary $[120,9,56]$ Codes Having an Automorphism of Order 3 and Associated SDP Designs

The number of known inequivalent binary self-complementary $[120,9,56]$ codes (and hence the number of known binary self-complementary $[136,9,64]$ codes) is increased from 25 to 4668 by showing that there are exactly 4650 such inequivalent codes with an automorphism of order 3. This implies that there are at least 4668 nonisomorphic quasi-symmetric SDP designs with parameters ($v=120$, $k=56$, $\lambda=55$) and as many SDP designs with parameters ($v=136$, $k=64$, $\lambda=56$).