construct/mc hadamard
construct/mc hadamard: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Find two sequences x 0..100 and y 0..100 with entries in {-1, +1} (a Legendre pair of length 101) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..50: sum {i=0}^{100} x i x (i+k) mod 101 + sum…
The task
Find two sequences x[0..100] and y[0..100] with entries in {-1, +1} (a Legendre pair of length 101) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..50: sum_{i=0}^{100} x[i]*x[(i+k) mod 101] + sum_{i=0}^{100} y[i]*y[(i+k) mod 101] = -2.