Replace each $-1$ with $0$. Then the matrix you look for is the adjacency matrix of a graph with a given degree sequence $r_1, r_2, \dots$. Reconstruction of such a graph (and its adjacency matrix) is known as the *graph realization* problem. E.g., see [Wikipedia](https://en.wikipedia.org/wiki/Graph_realization_problem) or [this webpage](https://piperfw.github.io/degreeSequences/) for additional details and solutions.