A new distance-regular graph of diameter 3 on 1024 vertices
arXiv:1806.07069 · doi:10.1007/s10623-019-00609-w
Abstract
The dodecacode is a nonlinear additive quaternary code of length . By puncturing it at any of the twelve coordinates, we obtain a uniformly packed code of distance . In particular, this latter code is completely regular but not completely transitive. Its coset graph is distance-regular of diameter three on vertices, with new intersection array . The automorphism groups of the code, and of the graph, are determined. Connecting the vertices at distance two gives a strongly regular graph of (previously known) parameters . Another strongly regular graph with the same parameters is constructed on the codewords of the dual code. A non trivial completely regular binary code of length is constructed.