Linear Independence of Random Boolean Tensor Powers at the Dimension Threshold

Kyle Luh

Let $d\ge 1$ be fixed and let \[ D(n,d) := \sum_{j=0}^{d} \binom{n-1}{j}. \] We show that if $x^{(1)},\dots ,x^{(m)}$ are independent uniform points of $\{\pm 1{\}}^n$ then unifor…