Welcome to the Ring Kingdom.
Ring code
Encodes \(K\) states (codewords) in \(n\) coordinates over a ring \(R\).
Parents:
Error-correcting code (ECC).
Parent of:
\(R\)-linear code.
\(R\)-linear code
A code of length \(n\) over a ring \(R\) is \(R\)-linear if it is a submodule of \(R^n\).
Parents:
Ring code.
Parent of:
Quaternary code over \(\mathbb{Z}_4\).
Quaternary code over \(\mathbb{Z}_4\)
A linear code encoding \(K\) states (codewords) in \(n\) coordinates over the ring \(\mathbb{Z}_4\) of integers modulo 4.
Parents:
\(R\)-linear code.