Parity-check tensor-product code[1]
Description
A \(q\)-ary linear code constructed out of two \(q\)-ary linear codes with parity-check matrices \(H_A,H_B\) such that its parity-check matrix is \(H_A \otimes H_B\). Its dual has parity-check matrix \(G_A\otimes G_B\), where \(G_{A,B}\) are the generator matrices of the two underlying codes [2].Notes
See Ref. [3] for an exposition.Cousin
- Tensor-product code— Tensor-product codewords (parity-check tensor-product parity-check matrices) are constructed via an outer product of the underlying codes (parity-check matrices).
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Parents
Parity-check tensor-product code
References
- [1]
- J. Wolf, “On codes derivable from the tensor product of check matrices”, IEEE Transactions on Information Theory 11, 281 (1965) DOI
- [2]
- D. Ostrev, D. Orsucci, F. Lázaro, and B. Matuz, “Classical product code constructions for quantum Calderbank-Shor-Steane codes”, Quantum 8, 1420 (2024) arXiv:2209.13474 DOI
- [3]
- J. K. Wolf, “An Introduction to Tensor Product Codes and Applications to Digital Storage Systems”, 2006 IEEE Information Theory Workshop - ITW ’06 Chengdu 6 (2006) DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2025-02-20)
Cite as:
“Parity-check tensor-product code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/parity_check_tensor, arXiv:2606.11484