A quasi-perfect code is a code whose covering radius is one greater than its packing radius. For minimum Hamming
distance 
,
the packing radius is 
, where 
is the floor function.
Thus the disjoint Hamming balls of packing radius leave uncovered words, but enlarging
their radius by one covers every word. This differs from a perfect
code, whose packing and covering radii are equal (Maharaj 2026).
The quaternary Preparata code for odd 
, including the octacode,
is quasi-perfect in the Hamming distance, with
packing radius one and covering radius two (Maharaj 2026).
