Concept of Isomorphisms and Automorphisms of a Balanced Incomplete Block Design

An algebraic approach can be used to construct balanced incomplete block design (BIBD) with the basic knowledge of group, ring, and field algebra. This paper aims at exploring the concept of isomorphism and automorphism of a balanced incomplete block designs (BIBD). Two balanced incomplete block designs were used to explore the above - stated aim. The results show that the design obtained from is isomorphic to each other under the defined mapping and automorphic by the mapping . We also used a block design where is a bijection which was shown to be isomorphic and automorphic design. We established a theorem to proof that any three blocks of BIBD is an equivalence classes of isomorphism. We, therefore conclude that any sets of balanced incomplete block design can be isomorphism and automorphism to each other.