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).
Decoder up to half of the minimum distance for NSC codes .
- Generalized RM (GRM) code — Applying a special case of the matrix-product procedure yields GRM codes .
- True Galois-qudit stabilizer code — Hermitian self-orthogonal matrix-product codes over \(GF(q^2)\) can be used to construct true stabilizer codes .
- T. Blackmore and G. H. Norton, “Matrix-Product Codes over ? q”, Applicable Algebra in Engineering, Communication and Computing 12, 477 (2001) DOI
- 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
- M. Cao and J. Cui, “Construction of new quantum codes via Hermitian dual-containing matrix-product codes”, Quantum Information Processing 19, (2020) DOI
- X. Liu, H. Liu, and L. Yu, “On New Quantum Codes From Matrix Product Codes”, (2021) arXiv:1604.05823
Page edit log
- Victor V. Albert (2022-07-21) — most recent
“Matrix-product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/matrix_product