The independence number of the orthogonality graph in dimension \(2^k\) (Q2300165)

The authors determine the independence number of the orthogonality graph on \(2^k\)-dimensional hypercubes. This result is related to a question stated by \textit{V. Galliard} [Classical pseudo-telepathy and colouring graphs. Zürich: ETH Zürich (Dipl. Thesis) (2001)], who is motivated by a problem in quantum information theory. The applied method is a modification of a rank argument due to \textit{P. Frankl} [Combinatorica 6, 279--285 (1986; Zbl 0648.05031)] who showed the analogous result for \(4p^k\)-dimensional hypercubes, where \(p\) is an odd prime.