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On the Largest Subsets Avoiding the Diameter of $(0,\Pm 1)$-Vectors by Adachi, Saori; Nozaki, Hiroshi is a scholarly article available to read on EtoBox.

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Let $L_{mkl}\subset \mathbb{R}^{m+k+l}$ be the set of vectors which have $m$ of entries $-1$, $k$ of entries $0$, and $l$ of entries $1$. In this paper, we investigate the largest subset of $L_{mkl}$ whose diameter is smaller than that of $L_{mkl}$. The largest subsets for $m=1$, $l=2$, and any $k$ will be classified. From this result, we can classify the largest $4$-distance sets containing the Euclidean representation of the Johnson scheme $J(9,4)$. This was an open problem in Bannai, Sato, and Shigezumi (2012).

Author

Adachi, Saori; Nozaki, Hiroshi

Published

2015

Language

EN