A new distance-regular graph of diameter 3 on 1024 vertices

06/19/2018

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by   Minjia Shi, et al.

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The dodecacode is a nonlinear additive quaternary code of length 12. By puncturing it at any of the twelve coordinates, we obtain an uniformly packed code of distance 5. In particular, this latter code is completely regular but not completely transitive. Its coset graph is distance-regular of diameter three on 2^10 vertices, with intersection array {33,30,15;1,2,15}. The automorphism groups of the code, and of the graph, are determined. Connecting the vertices at distance two gives a strongly regular graph of parameters (2^10, 495,238, 240). Two non trivial completely regular binary codes are constructed in length 27 and 33.