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

Abstract

The weight distribution of the binary self-dual $[128,64]$ code being the extended code $C^{\ast }$ 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 $C^{\ast }$ have no self-dual $[128,64,d]$ neighbor with $d\in \{20,24\}$.

10 pages