construct/mc hadamard
construct/mc hadamard: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Find two sequences x 0..6 and y 0..6 with entries in {-1, +1} (a Legendre pair of length 7) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..3: sum {i=0}^{6} x i x (i+k) mod 7 + sum {i=0}^{6} y i…
The task
Find two sequences x[0..6] and y[0..6] with entries in {-1, +1} (a Legendre pair of length 7) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..3: sum_{i=0}^{6} x[i]*x[(i+k) mod 7] + sum_{i=0}^{6} y[i]*y[(i+k) mod 7] = -2.