In this paper, we aim at utilizing the Cayley tables demonstrated by the Authors[1] in the construction of a Generator/Parity check Matrix in standard form for a Code say C Our goal is achieved first by converting the Cayley tables in [1] using Mod2 arithmetic into a Matrix with entries from the binary field. Echelon Row operations are then performed (carried out) on the matrix in line with existing algorithms and propositions to obtain a matrix say G whose rows spans C and a matrix say H whose rows spans C⊥, the dual code of C, where G and H are given as, G = (Ik | X ) and H= ( -XT | In-k ). The report by Williem (2011) that the adjacency Matrix of a graph can be interpreted as the generator matrix of a Code [3] is in this context extended to the Cayley table which generates matrices from the permutations of points of the AUNU numbers of prime cardinality.