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Super-simple balanced incomplete block designs with block size 4 and index 8. (English) Zbl 1311.05021

In this paper, the authors investigate the existence of a super-simple \((v,4,8)\) balanced incomplete block designs (BIBDs). They prove that such a design exists if and only if \(v \equiv 1 \pmod 3\) and \(v \geq 19\). Also, they construct many super-simple \((v,4,8)\) BIBDs for these values of \(v\). Finally, the authors mention some applications of the results in coding theory (about optical orthogonal codes and superimposed codes).

MSC:

05B05 Combinatorial aspects of block designs
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