construct/mc hadamard
construct/mc hadamard: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Find two sequences x 0..4 and y 0..4 with entries in {-1, +1} (a Legendre pair of length 5) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..2: sum {i=0}^{4} x i x (i+k) mod 5 + sum {i=0}^{4} y i…
The task
Find two sequences x[0..4] and y[0..4] with entries in {-1, +1} (a Legendre pair of length 5) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..2: sum_{i=0}^{4} x[i]*x[(i+k) mod 5] + sum_{i=0}^{4} y[i]*y[(i+k) mod 5] = -2.