Hypercube code

Cousins

• Biorthogonal spherical code— Orthoplexes and hypercubes are dual to each other.
• Dual polytope code— Orthoplexes and hypercubes are dual to each other.
• \(\mathbb{Z}^n\) hypercubic lattice— 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 (a.k.a. Boolean hypercube) embedded into the unit \(n\)-sphere.
• Binary code— Binary strings are elements of the Hamming \(n\)-cube (a.k.a. Boolean hypercube).
• 24-cell code— The vertices of a 24-cell are a union of the vertices of a tesseract and a 16-cell [2; Exam. 2.6].
• \([[2^D,D,2]]\) hypercube quantum code— \([[2^D,D,2]]\) hypercube quantum code qubits are placed on vertices of a \(D\)-cube.
• \([[m 2^m / (m+1), 2^m / (m+1), 2\lfloor m/4 \rfloor + 1]]\) Khesin-Lu-Shor code— The encoder-respecting form of the \([[m 2^m / (m+1), 2^m / (m+1), 2\lfloor m/4 \rfloor + 1]]\) Khesin-Lu-Shor code is the graph of a hypercube in \(m = 2^r - 1\) dimensions, and input nodes in the graph are codewords of the \([2^r-1,2^r-r-1,3]\) Hamming code [3].
• \([[16,6,4]]\) Tesseract color code— Stabilizer generators of both types of the tesseract color code are supported on each cube of a tesseract [4,5].
• Hemicubic code