Self-orthogonal binary subspace
= Self-orthogonal binary subspace
{title2=$W\subseteq W^\perp$}
A <linear subspace> $W\subseteq\mathbb F_2^n$ is self-orthogonal if $u\cdot v=0$ for every $u,v\in W$. The standard <bilinear form> is <nondegenerate>, whence $\dim W+\dim W^\perp=n$ and $\dim W\leq\lfloor n/2\rfloor$. The condition with $u=v$ means every vector has even <Hamming weight>. Such a <binary linear code> gives the <linear algebra> behind the <Eventown theorem>.