The line explanation helps with the intuition. There are multiple graphical explanations, e.g. ‘tiling’ a plane with ‘circles’ of minimum size to ensure error correctability. If the plane is too small to hold all circles without overlaps, you only get error detection. If furthermore a data point lies within (or on the boundary) of such circles you also lose full error detection.
However my initial study of this topic was directly in finite fields, thereby developing an entirely different intuition. Hence this is a nice alternative explanation!
Last paragraph is most interesting: “Many of the intermediate results of the algorithm described above will be fractional numbers, and not integers! Arbitrary precision rational math is not something computers are good at (especially when doing matrix inversion, polynomial division, and interpolation), so to gain speed, you’ll need to use Galois Fields and finite math; it’s what Infectious uses.”