Super-simple (v, 5, 5) Designs*

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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 (v, 5, 5) balanced incomplete block design and show that such a design exists if and only if vJOURNAL/dccry/04.02/00123454-200603920-00004/OV0113/v/2017-10-10T023708Z/r/image-png 1 (mod 4) and v ≥ 17 except possibly when v = 21. Applications of the results to optical orthogonal codes are also mentioned.

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