Sphere-packing bound
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
Distance is a picture
A message is a corner of a cube and an error is a step along an edge. Everything a code can do is decided by how far apart the corners it uses are — and that is a fact about a drawing.
![The sixteen words of the [7,4] Hamming code. A table of sixteen seven-bit codewords with their data bits, parity bits and weights.](/f/the-sixteen-words-of-the-7-4-hamming-code-03f0d582.svg)
Sixteen spheres that fill a cube
A hundred and twenty-eight seven-bit words, sixteen of them chosen, and a ball of eight around each. Sixteen times eight is a hundred and twenty-eight exactly — so the balls tile the space with nothing left over, and the code wastes nothing at all.
Named alongside it
The objects these essays reach for when they reach for this one.
Error-correcting codeHamming distanceMinimum distanceCheck digitCode rateCosetCounting argumentHamming codeHypercubeMetricModular arithmeticParity