Matrix-based code 

Also known as Two-dimensional code.
Root code for the Matrix Kingdom

Description

Encodes \(K\) states (codewords) in an \(m\times n\)-dimensional matrix of coordinates over a field (e.g., the Galois field \(GF(q)\) or the complex numbers \(\mathbb{C}\)).

Parents

Children

Cousin

  • \(q\)-ary code — Elements of fields such as \(GF(p^{ml})\) can be written as \(m\)-dimensional vectors over \(GF(p^l)\) or \((m\times l)\)-dimensional matrices over \(GF(p)\). This idea is used to convert between ordinary block codes and matrix-based codes such as disk array codes and rank-metric codes.
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Zoo Code ID: matrices_into_matrices

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/matrices/matrices_into_matrices.yml.