Abstract
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 (?, 5, 5) balanced incomplete block design and show that such a design exists if and only if ? ? 1 (mod 4) and ? ? 17 except possibly when ? = 21. Applications of the results to optical orthogonal codes are also mentioned.
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