construct/mc hadamard
construct/mc hadamard: a task in MathConstructOptimize-Envs-harbor (Harbor dataset). Find two sequences x 0..82 and y 0..82 with entries in {-1, +1} (a Legendre pair of length 83) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..41: sum {i=0}^{82} x i x (i+k) mod 83 + sum…
The task
Find two sequences x[0..82] and y[0..82] with entries in {-1, +1} (a Legendre pair of length 83) such that (a) sum(x) = 1 and sum(y) = 1, and (b) for every k = 1..41: sum_{i=0}^{82} x[i]*x[(i+k) mod 83] + sum_{i=0}^{82} y[i]*y[(i+k) mod 83] = -2.