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arXiv · 1809.07553

On tight $4$-designs in Hamming association schemes

Alexander Gavrilyuk·Sho Suda·Janoš Vidali
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Abstract

We complete the classification of tight $4$-designs in Hamming association schemes $H(n,q)$, i.e., that of tight orthogonal arrays of strength $4$, which had been open since a result by Noda (1979). To do so, we construct an association scheme attached to a tight $4$-design in $H(n,q)$ and analyze its triple intersection numbers to conclude the non-existence in all open cases.

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Alexander Gavrilyuk, Sho Suda, Janoš Vidali. 2019-07-16. On tight $4$-designs in Hamming association schemes. https://arxiv.org/abs/1809.07553

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