Matrix-product code[1]
Description
Code constructed from \(M\) length-\(n\) \(q\)-ary codes \(C_1,\ldots,C_M\) and an \(M\times N\) \(q\)-ary matrix \(A\), yielding all matrix products \([c_1\,\cdots\,c_M]A\) with \(c_i\in C_i\) and \(N\geq M\). A prominent subclass is the case in which \(A\) is non-singular by columns (NSC).Decoding
Decoder up to half of the minimum distance for NSC codes [2].Cousin
- Hermitian Galois-qudit code— Hermitian self-orthogonal matrix-product codes over \(\mathbb{F}_{q^2}\) can be used to construct quantum codes via the Hermitian construction [3,4].
Member of code lists
Primary Hierarchy
Parents
Matrix-product code
Children
Applying a special case of the matrix-product procedure yields GRM codes [1].
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]
- 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 (2026-06-08) — most recent
- Victor V. Albert (2022-07-21)
Cite as:
“Matrix-product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/matrix_product, arXiv:2606.11484