construct/mc hadamard
construct/mc hadamard: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Find two sequences x 0..8 and y 0..8 with entries in {-1, +1} (a Legendre pair of length 9) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..4: sum {i=0}^{8} x i x (i+k) mod 9 + sum {i=0}^{8} y i…
The task
Find two sequences x[0..8] and y[0..8] with entries in {-1, +1} (a Legendre pair of length 9) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..4: sum_{i=0}^{8} x[i]*x[(i+k) mod 9] + sum_{i=0}^{8} y[i]*y[(i+k) mod 9] = -2.