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 .
- 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
- Xiusheng Liu, Hualu Liu, and Long Yu, “On New Quantum Codes From Matrix Product Codes”. 1604.05823
Zoo code information
“Matrix-product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/matrix_product