{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T11:15:55Z","timestamp":1763810155920,"version":"3.41.2"},"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>We investigate the minimum distance of the error correcting code formed by the\u00a0homomorphisms between two finite groups $G$ and $H$.\u00a0We prove some general structural\u00a0results on how the distance behaves with respect to natural group operations,\u00a0such as passing to subgroups and quotients, and taking products.\u00a0Our main result is a general formula for the distance when $G$ is\u00a0solvable or $H$ is nilpotent, in terms of the normal subgroup\u00a0structure of $G$ as well as the prime divisors of $|G|$ and $|H|$.\u00a0In particular, we show that in the above case, the distance is\u00a0independent of the subgroup structure of $H$.\u00a0We complement this by showing that, in general, the distance depends on the\u00a0subgroup structure of $H$.<\/jats:p>","DOI":"10.37236\/4322","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:33:35Z","timestamp":1578702815000},"source":"Crossref","is-referenced-by-count":3,"title":["Group Homomorphisms as Error Correcting Codes"],"prefix":"10.37236","volume":"22","author":[{"given":"Alan","family":"Guo","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,1,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i1p4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:39:03Z","timestamp":1579257543000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i1p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/4322","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,1,2]]},"article-number":"P1.4"}}