Tensor code

Description

Martix-based code constructed out of two linear binary or \(q\)-ary codes \(C_A,C_B\) in an outer-product construction denoted as \(C_A \otimes C_B\). The codewords are those matrices whose column vectors are in \(C_A\) and whose row vectors are in \(C_B\).

Notes

Tensor codes formed by two random linear codes are robustly testable [1][2].

Parent

Cousins

Zoo code information

Internal code ID: tensor

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: tensor

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

References

[1]
Irit Dinur et al., “Good Quantum LDPC Codes with Linear Time Decoders”. 2206.07750
[2]
Gleb Kalachev and Pavel Panteleev, “Two-sided Robustly Testable Codes”. 2206.09973

Cite as:

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/matrices/tensor.yml.