{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:52Z","timestamp":1753893832411,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>This paper considers three imprimitive distance-regular graphs with $486$ vertices and diameter $4$: the Koolen--Riebeek graph (which is bipartite), the Soicher graph (which is antipodal), and the incidence graph of a symmetric transversal design obtained from the affine geometry $\\mathrm{AG}(5,3)$ (which is both). It is shown that each of these is preserved by the same rank-$9$ action of the group $3^5:(2\\times M_{10})$, and the connection is explained using the ternary Golay code.<\/jats:p>","DOI":"10.37236\/8954","type":"journal-article","created":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T12:55:34Z","timestamp":1595940934000},"source":"Crossref","is-referenced-by-count":0,"title":["On the 486-Vertex Distance-Regular Graphs of Koolen-Riebeek and Soicher"],"prefix":"10.37236","volume":"27","author":[{"given":"Robert F.","family":"Bailey","sequence":"first","affiliation":[]},{"given":"Daniel R.","family":"Hawtin","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,7,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p13\/8130","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p13\/8130","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T12:55:51Z","timestamp":1595940951000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,24]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8954","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,7,24]]},"article-number":"P3.13"}}