\(R\)-linear code
Description
A code of length \(n\) over a ring \(R\) is \(R\)-linear if it is a submodule of \(R^n\).
Parents
- Ring code
- Linear code over \(G\) — \(R\)-linear codes are linear over \(G=R\) since rings are abelian groups under addition.
Children
- Linear \(q\)-ary code — Linear \(q\)-ary codes are \(GF(q)\)-linear.
- \(q\)-ary code over \(\mathbb{Z}_q\)
Page edit log
- Victor V. Albert (2022-03-04) — most recent
Cite as:
“\(R\)-linear code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/rings_linear
Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/rings/rings_linear.yml.