construct/mc hadamard
construct/mc hadamard: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Find two sequences x 0..26 and y 0..26 with entries in {-1, +1} (a Legendre pair of length 27) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..13: sum {i=0}^{26} x i x (i+k) mod 27 + sum…
The task
Find two sequences x[0..26] and y[0..26] with entries in {-1, +1} (a Legendre pair of length 27) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..13: sum_{i=0}^{26} x[i]*x[(i+k) mod 27] + sum_{i=0}^{26} y[i]*y[(i+k) mod 27] = -2.