perfect code

Let C be a linear ( (n,k,d)-code over 𝔽q.

The packing radius of C is defined to be the value


The covering radius of C is


with x𝔽qn and cC, and where δ denotes the Hamming distanceMathworldPlanetmathPlanetmath on 𝔽qn.

The code ( C is said to be perfect if r(C)=ρ(C).

The list of of linear perfect codes is very short, including only trivial codes, Hamming codes (i.e. ρ=1), and the binary and ternary Golay ( codes.

Title perfect code
Canonical name PerfectCode
Date of creation 2013-03-22 14:23:43
Last modified on 2013-03-22 14:23:43
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 5
Author mathcam (2727)
Entry type Definition
Classification msc 11T71
Defines packing radius
Defines covering radius