Abstract
In this paper we classify distance-regular graphs, including strongly regular graphs, admitting a transitive action of the linear groups $L(3,2)$, $L(3,3)$, $L(3,4)$ and $L(3,5)$ for which the rank of the permutation representation is at most 15. We give details about constructed graphs. In addition, we construct self-orthogonal codes from distance-regular graphs obtained in this paper.
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