Root code for the Group Kingdom
Description
Encodes \(K\) states (codewords) in coordinates labeled by elements of a group \(G\). The number of codewords may be infinite for infinite groups, so various restricted versions have to be constructed in practice.
Protection
Bounds for permutation codes, i.e., codes on the symmetric group \(G=S_n\), have been developed [1,2].
Parent
Children
- Sphere packing — Sphere-packing alphabets \(\mathbb{R}^n\) are infinite fields, which are groups under addition.
- Binary permutation-based code
- Linear code over \(G\)
- Mixed code
- Rank-modulation Gray code (RMGC) — Group-alphabet codes whose alphabet is based on the permutation group \(S_n\) are rank-modulation codes.
- Matrix-based code — Matrix-based code alphabets are fields, which are groups under addition.
- Ring code — A ring \(R\) is an Abelian group under addition.
Cousin
References
Page edit log
- Victor V. Albert (2022-03-24) — most recent
Cite as:
“Group-alphabet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/group_classical