Coding theory MOC

Perfect code

A -ary code of length in alphabet is said to be a perfect -error correcting code, or briefly a perfect code, iff¹ #m/def/code

• it has minimum distance ; and
• for every string there exists a unique codeword with .

equivalently, has a minimum distance and covering radius . See also Quasi-perfect code.

Properties

• Sphere packing condition for a perfect code
• The extended code of a linear perfect code is quasi-perfect.

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