construct/mc hadamard
construct/mc hadamard: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Find two sequences x 0..14 and y 0..14 with entries in {-1, +1} (a Legendre pair of length 15) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..7: sum {i=0}^{14} x i x (i+k) mod 15 + sum…
The task
Find two sequences x[0..14] and y[0..14] with entries in {-1, +1} (a Legendre pair of length 15) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..7: sum_{i=0}^{14} x[i]*x[(i+k) mod 15] + sum_{i=0}^{14} y[i]*y[(i+k) mod 15] = -2.