Reed Solomon codes are cool
Wow. I love explaining Reed Solomon codes and this didn't do it justice.<p>The basic concept is that if I give you five points all on the same line, you only need any two of them to reconstruct the line.<p>Reed Solomon doesn't use lines (it isn't optimal) and the geometry they use isn't the Cartesian plane (this requires infinite precision) - but this is what the codes do!<p>Just like it requires two points to reconstruct a line, three points are required to reconstruct a simple polynomial (degree 2). Reed Solomon uses "high degree polynomials" which require n+1 points to reconstruct the degree-n polynomial.<p>The codes take data, make a polynomial out of it, and then send points from the polynomial to the other side, which can interpolate it as soon as enough points are gathered!<p>All of this looks like impenetrable discretization and matrix operations if you just get a description of the algorithms, which makes it seem a lot less approachable than it is.