Ring code

Root code for the Ring Kingdom

Description

Encodes \(K\) states (codewords) in \(n\) coordinates over a finite ring \(R\).

Parents

Block code — Ring codes are block codes with \(\Sigma=R\).
Finite-dimensional error-correcting code (ECC)
Group-alphabet code — A ring \(R\) is an Abelian group under addition.

Children

\(q\)-ary code — Galois fields are rings under addition.
Pentacode
\(q\)-ary code over \(\mathbb{Z}_q\)
\(R\)-linear code

Page edit log

Victor V. Albert (2022-02-16) — most recent

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Zoo Code ID: rings_into_rings

Cite as:: “Ring code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rings_into_rings
BibTeX:: @incollection{eczoo_rings_into_rings, title={Ring code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/rings_into_rings} }

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Permanent link:: https://errorcorrectionzoo.org/c/rings_into_rings

Cite as:

“Ring code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rings_into_rings

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/rings/rings_into_rings.yml.

Block
ECC
Classical-quantum (c-q)
Finite ECC
Group-alphabet
\(q\)-ary
Pentacode
\(q\)-ary code over \(\mathbb{Z}_q\)
\(R\)-linear

Classical Domain

Quantum Domain

Classical-quantum Domain

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Error correction zoo by Victor V. Albert, Philippe Faist, and many contributors. This work is licensed under a CC-BY-SA License. See how to contribute.