Some Designs of Small Orders and Their Codes

The binary and ternary codes spanned by the rows of the point-by-block, pair-by-block, block-by-point incidence matrices of some 2-designs of small orders and their orthogonal complements are studied. Among some results, it is shown that if the code is properly chosen, then the weight distribution of the code serves as an appropriate design isomorphism invariant. The automorphism groups of the codes and the design are computed.