Description
A linear code encoding \(K\) states (codewords) in \(n\) coordinates over the ring \(\mathbb{Z}_4\) of integers modulo 4.
Notes
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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 linear quaternary codes over \(\mathbb{Z}_4\) 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]
- S. T. Dougherty, "Codes over rings." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
Page edit log
- Victor V. Albert (2022-03-04) — most recent
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