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Let be a linear -code over
.
The packing radius of is defined to be the value
The covering radius of is
with
and , and where denotes the Hamming distance on
.
The code is said to be perfect if
.
The list of classes of linear perfect codes is very short, including only trivial codes, Hamming codes (i.e. ), and the binary and ternary Golay codes.
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