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Galois-qudit HGP code

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.

Cousin

  • Linear \(q\)-ary code— Galois-qudit HGP codes are constructed out of two classical linear \(q\)-ary codes.

Member of code lists

Primary Hierarchy

Quantum Domain
Galois-qudit Kingdom
Galois-qudit codeQECC Quantum
Galois-qudit USt code
Galois-qudit stabilizer codeStabilizer Hamiltonian-based QECC Quantum
True Galois-qudit stabilizer code
Galois-qudit CSS codeCSS Stabilizer Hamiltonian-based QECC Quantum
Balanced product (BP) codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
Lifted-product (LP) code
Parents
Lifted-product (LP) code
Lifted-product codes for trivial lift are Galois-qudit hypergraph-product codes.
Galois-qudit HGP code
Children
Hypergraph product (HGP) code
Hypergraph product codes are Galois-qudit hypergraph-product codes for qudit dimension \(q=2\).
Galois-qudit expander code
Page edit log

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Zoo Code ID: galois_hypergraph_product

Cite as:
“Galois-qudit HGP code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/galois_hypergraph_product
BibTeX:
@incollection{eczoo_galois_hypergraph_product, title={Galois-qudit HGP code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/galois_hypergraph_product} }
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Permanent link:
https://errorcorrectionzoo.org/c/galois_hypergraph_product

Cite as:

“Galois-qudit HGP code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/galois_hypergraph_product

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/stabilizer/qldpc/balanced_product/galois_hypergraph_product.yml.