Code whose set of codewords forms an orbit of some reference codeword under a subgroup of the automorphism group, i.e., the group of distance-preserving transformations on the metric space defined with the code's alphabet.
- Error-correcting code (ECC) — Not all codes are group-orbit codes, and more generally one can classify codewords into orbits of the automorphism group .
- Linear code over \(G\) — Since codewords of a linear code over \(G\) form a group, any codeword \(c\) can be obtained from any other codeword via action of a codeword. This means that the set of codewords can be thought of as an orbit of a particular codeword under the group. For example, see [2; Thm. 8.4.2] for the binary case. However, group orbit codes do not have to be linear; see [2; Remark 8.4.3].
- Slepian group-orbit code — Slepian group-orbit codes are group-orbit codes on spheres. Binary group-orbit codes can be mapped into Slepian group-orbit codes via various mappings [2; Ch. 8].
- 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
- T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
Page edit log
- Victor V. Albert (2022-07-18) — most recent
“Group-orbit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/group_orbit