Coding Matrices for the Semi-Direct Product Groups

Abstract

We shall determine the coding matrix of the semi-direct product group $ G = C_{n} \rtimes_{\phi} C_{m} $ ; $ \phi : C_{m} \longrightarrow Aut(C_{n}) $ of two cyclic groups in order to generalize the known result for the dihedral group $D_{2n}$, which is known to be a semi-direct of the two cyclic groups $C_{n} \ , \ C_{2}$.

Keywords

• Code
• Group ring
• Ring of matrices
• Semi-direct product group

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