construct/mc hadamard
construct/mc hadamard: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Find two sequences x 0..46 and y 0..46 with entries in {-1, +1} (a Legendre pair of length 47) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..23: sum {i=0}^{46} x i x (i+k) mod 47 + sum…
The task
Find two sequences x[0..46] and y[0..46] with entries in {-1, +1} (a Legendre pair of length 47) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..23: sum_{i=0}^{46} x[i]*x[(i+k) mod 47] + sum_{i=0}^{46} y[i]*y[(i+k) mod 47] = -2.