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

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

Journal

Designs, Codes and Cryptography
ISSN: 0925-1022 , E-ISSN: 1573-7586

Output data

Year: 2019, Volume: 87, Number: 9, Pages: 2091-2101 Pages count : 11 DOI: 10.1007/s10623-019-00609-w

Tags

Distance-regular graphs, completely regular codes, uniformly packed codes, additive quaternary codes

Authors

Shi M. ¹ , Krotov D.S. ² , Solé P. ³

Affiliations

1	School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, China
2	Sobolev Institute of Mathematics, pr. Akademika Koptyuga 4, Novosibirsk, Russia 630090
3	4CNRS/LAGA, University of Paris 8, 2 rue de la Liberté, 93 526 Saint-Denis, France

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.

Shi M. , Krotov D.S. , Solé P.
A new distance-regular graph of diameter 3 on 1024 vertices
Designs, Codes and Cryptography. 2019. V.87. N9. P.2091-2101. DOI: 10.1007/s10623-019-00609-w WOS Scopus РИНЦ OpenAlex

Submitted:	Jun 26, 2018
Accepted:	Jan 10, 2019
Published online:	Jan 24, 2019

Web of science:	WOS:000483581300009
Scopus:	2-s2.0-85060695632
Elibrary:	41616075
OpenAlex:	W3105536874

DB	Citing
Web of science	10
Scopus	11
OpenAlex	10