Bounds on minors of binary matrices

We prove an upper bound on sums of squares of minors of {+1,−1} matrices. The bound is sharp for Hadamard matrices, a result due to de Launey and Levin (2009), but our proof is simpler. We give several corollaries relevant to minors of Hadamard matrices, and generalise a result of Turán on determinants of random {+1,−1} matrices.