{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T23:45:42Z","timestamp":1778111142809,"version":"3.51.4"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2007,9]]},"abstract":"<jats:p> Applications in quantum information theory and quantum tomography have raised current interest in complex Hadamard matrices. In this note we investigate the connection between tiling of Abelian groups and constructions of complex Hadamard matrices. First, we recover a recent, very general construction of complex Hadamard matrices due to Dita [2] via a natural tiling construction. Then we find some necessary conditions for any given complex Hadamard matrix to be equivalent to a Dita-type matrix. Finally, using another tiling construction, due to Szab\u00f3 [8], we arrive at new parametric families of complex Hadamard matrices of order 8, 12 and 16, and we use our necessary conditions to prove that these families do not arise with Dita's construction. These new families complement the recent catalogue [10] of complex Hadamard matrices of small order. <\/jats:p>","DOI":"10.1007\/s11080-007-9050-6","type":"journal-article","created":{"date-parts":[[2007,9,14]],"date-time":"2007-09-14T02:38:26Z","timestamp":1189737506000},"page":"247-263","source":"Crossref","is-referenced-by-count":14,"title":["Constructions of Complex Hadamard Matrices via Tiling Abelian Groups"],"prefix":"10.1142","volume":"14","author":[{"given":"M\u00e1t\u00e9","family":"Matolcsi","sequence":"first","affiliation":[{"name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, POB 127 H\u20131364 Budapest, Hungary"}]},{"given":"J\u00falia","family":"R\u00e9ffy","sequence":"additional","affiliation":[{"name":"Technical University Budapest (BME), Institute of Mathematics, Department of Analysis, Hungary"}]},{"given":"Ferenc","family":"Sz\u00f6ll\u0151si","sequence":"additional","affiliation":[{"name":"Technical University Budapest (BME), Hungary"}]}],"member":"219","published-online":{"date-parts":[[2012,4,17]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/20\/008"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-005-5069-7"},{"key":"rf4","unstructured":"U.\u00a0Haagerup, Operator Algebras and Quantum Field Theory (Rome), Orthogonal maximal abelian *-subalgebras of the n \u00d7 n matrices and cyclic n-roots (MA International Press, Cambridge, 1996)\u00a0pp. 296\u2013322."},{"key":"rf5","first-page":"281","author":"Kolountzakis M. N.","journal-title":"Collect. Math."},{"key":"rf6","first-page":"519","volume":"18","author":"Kolountzakis M. N.","journal-title":"Forum Math."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1017\/S0017089500002202"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(85)90071-8"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2006.03.004"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s11080-006-8220-2"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/34\/35\/332"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1007\/s11080-007-9050-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:59:55Z","timestamp":1565107195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1007\/s11080-007-9050-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9]]},"references-count":10,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,4,17]]},"published-print":{"date-parts":[[2007,9]]}},"alternative-id":["10.1007\/s11080-007-9050-6"],"URL":"https:\/\/doi.org\/10.1007\/s11080-007-9050-6","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9]]}}}