Are location in BRIEF feature descriptor reused?
When using a randomized pattern in BRIEF, this means that you computed random positions inside the patch once in an offline procedure, then used these random locations every time you computed the descriptors. This makes sense, as it means that when comparing descriptors you will actually compare the same locations, it's simply that the sampling pattern was not obtained by some regular or geometric scheme (which is probably what makes it a bit more generic than hand-crafted patterns).
For example, here is the sampling pattern used by OpenCV.