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Ring code

Root code for the Ring Kingdom

Description

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

Member of code lists

Primary Hierarchy

Classical Domain
Ring Kingdom
Parents
Block codeECC
Ring codes are block codes with \(\Sigma=R\).
Finite-dimensional error-correcting code (ECC)ECC
Group-alphabet codeECC
A ring \(R\) is an Abelian group under addition.
Ring code
Children
\(q\)-ary codeSelf-dual additive Linear \(q\)-ary Gray Evaluation Self-dual linear QR Projective geometry Tanner \(q\)-ary LDPC Divisible AG Editing GRM OA Perfect Nearly perfect Perfect binary Combinatorial design MDS GRS Balanced
Galois fields are rings under addition.
Pentacode
\(q\)-ary code over \(\mathbb{Z}_q\)\(q\)-ary linear code over \(\mathbb{Z}_q\)
\(R\)-linear codeLinear \(q\)-ary Gray Evaluation MDS GRS GRM QR Projective geometry Tanner \(q\)-ary LDPC Divisible Self-dual additive Self-dual linear \(q\)-ary linear code over \(\mathbb{Z}_q\)
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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.