Group code

In computer science, group codes are a type of code. Group codes consist of ${\displaystyle n}$ linear block codes which are subgroups of ${\displaystyle G^{n}}$, where ${\displaystyle G}$ is a finite Abelian group.

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

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