## Description

Code designed for transmission of classical information through classical channels in a robust way.

## Parent

- Operator-algebra error-correcting code — Any ECC can be embedded into a quantum Hilbert space, and thus passed through a quantum channel, by associating elements of the alphabet with basis vectors in a Hilbert space over the complex numbers. For example, a bit of information can be embedded into a two-dimensional vector space by associating the two bit values with two basis vectors for the space.

## Children

- Group-alphabet code
- Block code
- Generalized concatenated code
- Parallel concatenated code
- Finite-dimensional error-correcting code (ECC)
- Group-orbit code — Not all codes are group-orbit codes, and more generally one can classify codewords into orbits of the automorphism group [1].
- Random code

## Cousin

- Quantum error-correcting code (QECC) — Error-correction conditions can similarly be formulated for classical codes [2; Sec. 3], although they are not as widely as used as those for quantum codes.

## References

- [1]
- J. H. Conway and N. J. A. Sloane, “Orbit and coset analysis of the Golay and related codes”, IEEE Transactions on Information Theory 36, 1038 (1990) DOI
- [2]
- B. Yoshida, “Decoding the Entanglement Structure of Monitored Quantum Circuits”, (2021) arXiv:2109.08691

## Page edit log

- Victor V. Albert (2022-11-06) — most recent

## Cite as:

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

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