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zbMATH Open
Article . 2022
Data sources: zbMATH Open
https://dx.doi.org/10.48550/ar...
Article . 2021
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
DBLP
Article . 2021
Data sources: DBLP
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A database of quantum codes

Authors: Nuh Aydin; Peihan Liu; Bryan Yoshino;

A database of quantum codes

Abstract

Quantum error correcting codes (QECC) is becoming an increasingly important branch of coding theory. For classical block codes, a comprehensive database of best known codes (codetables.de) exists which is available online at \cite{codetables}. The same database contains data on best known quantum codes as well, but only for the binary field. There has been an increased interest in quantum codes over larger fields with many papers reporting such codes in the literature. However, to the best of our knowledge, there is no database of best known quantum codes for most fields. We established a new database of QECC that includes codes over $\mathbb{F}_{q^2}$ for $q\leq 29$. We also present several methods of constructing quantum codes from classical codes based on the CSS construction. We have found dozens of new quantum codes that improve the previously known parameters and also hundreds new quantum codes that did not exist in the literature.

Keywords

CSS construction, constacyclic codes, FOS: Computer and information sciences, Bounds on codes, Quantum cryptography (quantum-theoretic aspects), quantum error-correcting codes, polycyclic codes, Other types of codes, Computer Science - Information Theory, Information Theory (cs.IT), Linear codes (general theory)

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    3
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green
gold