Super-simple (ν, 5, 5) Designs

Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. In this article, we investigate the existence of a super-simple (ν, 5, 5) balanced incomplete block design and show that such a design exists if and only if ν ≡ 1 (mod 4) and ν ≥ 17 except possibly when ν = 21. Applications of the results to optical orthogonal codes are also mentioned. Research supported by NSERC grant 239135-01.