= Quantum Hamming bound
{title2=$\sum_{j=0}^t3^j\binom nj\leq2^{n-k}$}
For unknown-location <Pauli operators> of weight at most $t$, there are $N(t)=\sum_{j=0}^t3^j\binom nj$ physically distinct errors modulo phase, including the identity. A <nondegenerate quantum code> assigns them mutually orthogonal error-image subspaces, each of dimension $2^k$, within the $2^n$-dimensional physical <Hilbert space>. Hence $N(t)2^k\leq2^n$. The hypothesis of nondegeneracy is essential to this dimension count.
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