1 Answers
In coding theory, group codes are a type of code. Group codes consist of n {\displaystyle n} linear block codes which are subgroups of G n {\displaystyle G^{n}} , where G {\displaystyle G} is a finite Abelian group.
A systematic group code C {\displaystyle C} is a code over G n {\displaystyle G^{n}} of order | G | k {\displaystyle \left|G\right|^{k}} defined by n − k {\displaystyle n-k} homomorphisms which determine the parity check bits. The remaining k {\displaystyle k} bits are the information bits themselves.