{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T20:39:24Z","timestamp":1772224764022,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A code $C$ in the Hamming graph $\\varGamma=H(m,q)$ is $2$-neighbour-transitive if ${\\rm Aut}(C)$ acts transitively on each of $C=C_0$, $C_1$ and $C_2$, the first three parts of the distance partition of $V\\varGamma$ with respect to $C$. Previous classifications of families of $2$-neighbour-transitive codes leave only those with an affine action on the alphabet to be investigated. Here, $2$-neighbour-transitive codes with minimum distance at least $5$ and that contain ``small'' subcodes as blocks of imprimitivity are classified. When considering codes with minimum distance at least $5$, completely transitive codes are a proper subclass of $2$-neighbour-transitive codes. This leads, as a corollary of the main result, to a solution of a problem posed by Giudici in 1998 on completely transitive codes.<\/jats:p>","DOI":"10.37236\/8040","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T10:05:14Z","timestamp":1581069914000},"source":"Crossref","is-referenced-by-count":2,"title":["$2$-Neighbour-Transitive Codes with Small Blocks of Imprimitivity"],"prefix":"10.37236","volume":"27","author":[{"given":"Neil I.","family":"Gillespie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel R.","family":"Hawtin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cheryl E.","family":"Praeger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,1,29]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p42\/8028","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p42\/8028","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T10:05:14Z","timestamp":1581069914000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,29]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8040","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,29]]},"article-number":"P1.42"}}