= Perfect quantum error-correcting code
{title2=$2^k\sum_{j=0}^t3^j\binom nj=2^n$}
A <nondegenerate quantum code> is perfect at correction radius $t$ if its distinct correctable <Pauli error> images exhaust the physical <Hilbert space>. Each image has dimension $2^k$, and their <orthogonal direct sum> is the whole $2^n$-dimensional space precisely when the <quantum Hamming bound> is an equality. This perfectness concerns unknown-location errors of weight at most $t$; it does not imply correction of every higher-weight error.
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