Matrix-product code[1]

Description

Code constructed using a concatenation procedure that yields a code consisting of all products of codewords in \(M\) length-\(n\) \(q\)-ary codes and an \(M\times N\) \(q\)-ary matrix with \(N\geq M\). A prominent subclass is the case with \(A\) is non-singular by columns (NSC).

Decoding

Decoder up to half of the minimum distance for NSC codes [2].

Parent

Child

Cousin

References

[1]
T. Blackmore and G. H. Norton, “Matrix-Product Codes over ? q”, Applicable Algebra in Engineering, Communication and Computing 12, 477 (2001). DOI
[2]
F. Hernando, K. Lally, and D. Ruano, “Construction and decoding of matrix-product codes from nested codes”, Applicable Algebra in Engineering, Communication and Computing 20, 497 (2009). DOI
[3]
M. Cao and J. Cui, “Construction of new quantum codes via Hermitian dual-containing matrix-product codes”, Quantum Information Processing 19, (2020). DOI
[4]
Xiusheng Liu, Hualu Liu, and Long Yu, “On New Quantum Codes From Matrix Product Codes”. 1604.05823

Zoo code information

Internal code ID: matrix_product

Your contribution is welcome!

on github.com (edit & pull request)

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Zoo Code ID: matrix_product

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

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/q-ary_digits/matrix_product.yml.