Description
Spherical \((n,2^n,4/n)\) code whose codewords are vertices of an \(n\)-cube, i.e., all permutations and negations of the vector \((1,1,\cdots,1)\), up to normalization.
Parents
- Polytope code — Hypercube codewords in 2 (3, 4, \(n\)) dimensions form the vertices of a triangle (sqaure, cube, \(n\)-cube).
- Lattice-shell code — Hypercube codewords form the minimal lattice shell code of the \(\mathbb{Z}^n\) hypercubic lattice when the lattice is shifted such that the center of a hypercube is at the origin.
- Polyphase code
Cousins
- Biorthogonal spherical code — Orthoplexes and hypercubes are dual to each other.
- \(\mathbb{Z}^n\) hypercubic lattice code — Hypercube codewords form the minimal lattice shell code of the \(\mathbb{Z}^n\) hypercubic lattice when the lattice is shifted such that the center of a hypercube is at the origin.
- Binary antipodal code — Binary antipodal codes are subcodes of a hypercube code since the hypercube code corresponds to the Hamming \(n\)-cube embedded into the unit \(n\)-sphere.
- \([[2^D,D,2]]\) hypercube quantum code — \([[2^D,D,2]]\) hypercube quantum code qubits are placed on vertices of a \(D\)-cube.
- Hemicubic code
Page edit log
- Victor V. Albert (2024-03-21) — most recent
Cite as:
“Hypercube code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/hypercube