Alternative names: Galois-qudit quantum hypergraph (QHG) code, Galois-qudit Tillich-Zemor product code.
Description
A member of a family of Galois-qudit CSS codes whose stabilizer generator matrix is obtained from a hypergraph product of two classical linear \(q\)-ary codes.Cousins
- Linear \(q\)-ary code— Galois-qudit HGP codes are constructed out of two classical linear \(q\)-ary codes.
- Two-block group-algebra (2BGA) codes— A 2BGA code \(LP(a,b)\) is constructible as a hypergraph-product code when the support subgroups generated by \(a\) and \(b\) are disjoint. In that case, the commuting matrices simultaneously acquire hypergraph-product Kronecker-product form, and the code can be obtained from a pair of classical group-algebra codes [1; Statements 8 and 12].
Primary Hierarchy
Balanced product (BP) codeGeneralized homological-product CSS Stabilizer Hamiltonian-based QECC Quantum
Parents
Lifted-product codes for trivial lift are Galois-qudit hypergraph-product codes.
Galois-qudit HGP code
Children
Hypergraph product codes are Galois-qudit hypergraph-product codes for qudit dimension \(q=2\).
References
- [1]
- H.-K. Lin and L. P. Pryadko, “Quantum two-block group algebra codes”, (2023) arXiv:2306.16400
Page edit log
- Victor V. Albert (2024-10-22) — most recent
Cite as:
“Galois-qudit HGP code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/galois_hypergraph_product