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.
Parent
Children
- Sphere packing — Sphere-packing alphabets \(\mathbb{R}^n\) are infinite fields, which are groups under addition.
- Linear code over \(G\)
- Mixed code
- Code in permutations — Codes in permutations are group-alphabet codes for the symmetric group \(G=S_n\).
- 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
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