Group code

In Error correction and detection, Group codes are $n$ length Linear block codes which are subgroups of $G^{n}$, where $G$ is a Finite Abelian group.

A systematic group code $C$ is a code over $G^{n}$ of order $\left|G\right|^{k}$ defined by $n-k$ homomorphisms which determine the parity check bits. The remaining $k$ bits are the information bits themselves.