MDS, Hermitian almost MDS, and Gilbert–Varshamov quantum codes from generalized monomial-Cartesian codes
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Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/173364
comunitat-uji-handle3:10234/173369
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Title
MDS, Hermitian almost MDS, and Gilbert–Varshamov quantum codes from generalized monomial-Cartesian codesDate
2024-03-01Publisher
Springer NatureISSN
1570-0755; 1573-1332Bibliographic citation
Barbero-Lucas, B., Hernando, F., Martín-Cruz, H. et al. (2024) MDS, Hermitian almost MDS, and Gilbert–Varshamov quantum codes from generalized monomial-Cartesian codes. Quantum Inf Process 23, 86.Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
We construct new stabilizer quantum error-correcting codes from generalized monomial-Cartesian codes. Our construction uses an explicitly defined twist vector, and we present formulas for the minimum distance and ... [+]
We construct new stabilizer quantum error-correcting codes from generalized monomial-Cartesian codes. Our construction uses an explicitly defined twist vector, and we present formulas for the minimum distance and dimension. Generalized monomial-Cartesian codes arise from polynomials in m variables. When
our codes are MDS, and when and our lower bound for the minimum distance is 3, the codes are at least Hermitian almost MDS. For an infinite family of parameters, when we prove that our codes beat the Gilbert–Varshamov bound. We also present many examples of our codes that are better than any known code in the literature. [-]
Is part of
Quantum Information Processing, Vol. 23 (2024)Funder Name
IReL Consortium | Ministerio de Ciencia, Innovación y Universidades / Agencia Estatal de Investigación (AEI) | European Union NextGenerationEU/PRTR | Universitat Jaume I
Project code
10.13039/501100011033 | TED2021-130358B-I00 | PID2022-138906NB-C22 | UJI-B2021-02 | GACUJIMB/2023/03 | PREDOC/2020/39
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info:eu-repo/semantics/openAccess
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