Perfect codes \((n,K,d)_q\) are those for which balls of Hamming radius \(t=\left\lfloor (d-1)/2\right\rfloor\) exactly fill the space of all \(n\) \(q\)-ary strings. Quasi-perfect codes are those for which balls of Hamming radius \(t\) are disjoint, while balls of radius \(t+1\) cover the space with possible overlaps. In other words, any \(q\)-ary string is at most \(t+1\) bit flips away from a codeword of a quasi-perfect code.
Correct errors of weight \(t\) as well as some errors of weight \(t+1\).
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Zoo code information
“Quasi-perfect code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quasi_perfect