Wow. I love explaining Reed Solomon codes and this didn't do it justice.
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.
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!
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.
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!
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.
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.
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!
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.
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!
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.