A new distance-regular graph of diameter 3 on 1024 vertices - Archive ouverte HAL
Article Dans Une Revue Designs, Codes and Cryptography Année : 2019

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

Résumé

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 vertices, with new 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 (previously known) parameters (2 10 , 495, 238, 240). 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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Dates et versions

hal-02411616 , version 1 (17-12-2019)

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Minjia Shi, Denis S. Krotov, Patrick Sole. A new distance-regular graph of diameter 3 on 1024 vertices. Designs, Codes and Cryptography, 2019, 87, pp.2091 - 2101. ⟨10.1007/s10623-019-00609-w⟩. ⟨hal-02411616⟩
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