I have a quadratic form $Q(u) = \langle Du , u \rangle = 0$, where $D$ is circulant-symmetric from $\mathbb{R}^{n \times n}$ $D$ has all entries $0$ or $1$ except the diagonal which a negative real number $a$. It is known there are solutions to $Q(u)$ such that $u$ is just from $\{0,1\}^{n}$. I have a point $v \in \mathbb{R}^{n}$ on the quadratic form. How can I find an estimate of the distance to the closest point $w$ from $v$ such that the point $w$ satisfies $Q(w) = 0$ and has coordinates just $0$ or $1$? Are there any connections to lattice decoding? (Will simple rounding work?)
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