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

M Shi, DS Krotov, P Solé - Designs, Codes and Cryptography, 2019 - Springer
Designs, Codes and Cryptography, 2019Springer
The dodecacode is a nonlinear additive quaternary code of length 12. By puncturing it at any
of the twelve coordinates, we obtain a 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 2 10 vertices, with new intersection array {33, 30, 15; 1, 2,
15\} 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 …
Abstract
The dodecacode is a nonlinear additive quaternary code of length 12. By puncturing it at any of the twelve coordinates, we obtain a 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 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 33 is constructed.
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