{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T09:15:51Z","timestamp":1776849351230,"version":"3.51.2"},"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>All generalized Hadamard matrices of order 18 over a group of order 3, $H(6,3)$, are enumerated in two different ways: once, as class regular symmetric $(6,3)$-nets, or symmetric transversal designs on 54 points and 54 blocks with a group of order 3 acting semi-regularly on points and blocks, and secondly, as collections of full weight vectors in quaternary Hermitian self-dual codes of length 18. The second enumeration is based on the classification of Hermitian self-dual $[18,9]$ codes over $GF(4)$, completed in this paper. It is shown that up to monomial equivalence, there are 85 generalized Hadamard matrices $H(6,3)$, and 245 inequivalent  Hermitian self-dual codes of length 18 over $GF(4)$.<\/jats:p>","DOI":"10.37236\/443","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:58:45Z","timestamp":1578715125000},"source":"Crossref","is-referenced-by-count":6,"title":["Classification of Generalized Hadamard Matrices $H(6,3)$ and Quaternary Hermitian Self-Dual Codes of Length 18"],"prefix":"10.37236","volume":"17","author":[{"given":"Masaaki","family":"Harada","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clement","family":"Lam","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akihiro","family":"Munemasa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladimir D.","family":"Tonchev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2010,12,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r171\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r171\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:19:04Z","timestamp":1579303144000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r171"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/443","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12,10]]},"article-number":"R171"}}