Binary self-dual code contains the all-ones word
= Binary self-dual code contains the all-ones word
For a binary <self-dual code>, every word $c$ satisfies $c\cdot c=0$. In characteristic two this is $\sum_i c_i=0$, so the all-ones word is orthogonal to every <codeword> and lies in the <dual code>, hence the code itself. The <dual code> <dimension> identity gives even length and half-length <dimension>.