  The $n$-dimensional hypercube $Q_n$ is a graph with vertex set $\{0,1\}^n$
and there is an edge between two vertices if they differ in exactly one
coordinate. For any graph $H$, define $\text{ex}(Q_n,H)$ to be the maximum
number of edges of a subgraph of $Q_n$ without a copy of $H$. In this short
note, we prove that for any $n \in \mathbb{N}$ $$\text{ex}(Q_n, C_{10}) > 0.024
\cdot e(Q_n).$$ Our construction is strongly inspired by the recent
breakthrough work of Ellis, Ivan, and Leader, who showed that "daisy"
hypergraphs have positive Tur\'an density with an extremely clever and simple
linear-algebraic argument.
