Let $G\in \Bbb Z^{n\times n}$ be a unimodular matrix.
Are there any efficient algorithms to find the maximum norm of a vector $v$ that satisfies $\langle\Delta(v),v\rangle=0$ over all vectors $v\in xG$ within a ball of radius $r$ at the origin, where $x\in \Bbb Z^{n}$ and $\Delta\in \Bbb Z^{n\times n}$ is another unimodular matrix?
$\Delta$ is a tensor product of matrices of the form: $$ \begin{matrix} -1 & 1 & \dots & 1\\ 0 & a_{11} & \dots & a_{1n} \\ \vdots & \vdots & \ddots & \vdots\\ 0 & a_{n1} & \dots & a_{nn} \end{matrix} $$ where the $a_{ii}$s form a self-adjoint circulant matrix.