The weight distribution of the self-dual [ 128 , 64 ] polarity design code

The weight distribution of the binary self-dual [128 , 64] code being the extended code C ∗ of the code C spanned by the incidence vectors of the blocks of the polarity design in PG( 6 , 2 ) [11] is computed. It is shown also that R(3 , 7) and C ∗ have no self-dual [128 , 64 , d] neighbor with d ∈ {20 , 24}