Hamming Sphere-Packing Bound
Pack Hamming balls to see which error-correcting code sizes are impossible.
Free theory articlePack Hamming balls to see which error-correcting code sizes are impossible.
Concept & interpretation
The Hamming Sphere-Packing Bound provides a fundamental limitation on the parameters of an error-correcting code. It states that the total volume of non-overlapping Hamming spheres around each codeword must not exceed the total volume of the ambient space.
Experiment
In the Hamming Sphere-Packing Bound module, you can adjust the parameters:
- Select Bits n to change the space dimensionality.
- Select Errors t to change the radius of the Hamming balls.
- Select Codewords M to see if that many non-overlapping spheres can fit in the space.
Observe the "Verdict" output. When the "Used sphere budget" exceeds the "Binary space size", the slack becomes negative, and such a code is "Ruled out".