collection
Binary quantum Hamming CSS code
A binary CSS family whose check block is the parity-check matrix of a classical binary Hamming code. The constructor labels columns by all nonzero r-bit vectors and uses the same block for X and Z checks. This is the CSS family containing the Steane and fifteen-qubit Hamming blocks, not the distinct non-CSS perfect-code family with a similar name.
Scoped completion
Completion belongs to an entity, not the whole page
eczoo-entity:quantum_hamming_css#collectionT1 — preserved
Verified formal skeleton
The formal core and displayed claims are provenance-checked. Unlisted facets are not yet surveyed, not negative results.
One orienting visual
Orienting view
Inspect constructor-derived qubits, stabilizers, and logical paths without leaving the entry. Visual instance: r3
At a glance
Executable-target parameters
form: collection formal target: css
Constructor variables
r- Hamming parity-check row count; integer at least 3
Reference instances
| Instance | n | k | d |
|---|---|---|---|
| r3 | n=7 verified | k=1 verified | d=3 verified |
| r4 | n=15 verified | k=7 verified | d=3 verified |
| r5 | n=31 verified | k=21 verified | d=3 verified |
Scientific scope
Source, page, and formal object are separate identities
Primary entity: eczoo-entity:quantum_hamming_css#collection. Formalization target: eczoo-entity:quantum_hamming_css#collection. Legacy vocabulary: exact family projection.
Source/entity binding: clean.