Quaternary code over \(\mathbb{Z}_4\)

Description

A linear code encoding \(K\) states (codewords) in \(n\) coordinates over the ring \(\mathbb{Z}_4\) of integers modulo 4.

Notes

Code Database, including quasi-cyclic and quasi-twisted codes [1].

Parent

Child

Cousins

  • Niemeier lattice code — Niemeier lattice codes can be constructed from quaternary codes over \(\mathbb{Z}_4\) via Construction \(A_4\) [2].
  • Melas code — The even-weight subcode of the Melas code can be lifted to a code over \(\mathbb{Z}_4\) [3].
  • Reed-Muller (RM) code — RM codes are images of ring-linear quaternary codes under the Gray map ([4], Sec. 6.3).

References

[1]
N. Aydin, Y. Lu, and V. R. Onta, “An Updated Database of \(\mathbb{Z}_4\) Codes”, (2022) arXiv:2208.06832
[2]
A. Bonnecaze et al., “Niemeier lattices and Type II codes over Z4”, Discrete Mathematics 205, 1 (1999) DOI
[3]
A. Alahmadi et al., “On the lifted Melas code”, Cryptography and Communications 8, 7 (2015) DOI
[4]
W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
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Zoo Code ID: quaternary_over_z4

Cite as:
“Quaternary code over \(\mathbb{Z}_4\)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quaternary_over_z4
BibTeX:
@incollection{eczoo_quaternary_over_z4, title={Quaternary code over \(\mathbb{Z}_4\)}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quaternary_over_z4} }
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Cite as:

“Quaternary code over \(\mathbb{Z}_4\)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quaternary_over_z4

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/rings/quaternary_over_z4.yml.