{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:08:37Z","timestamp":1757617717992,"version":"3.44.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s10623-025-01608-w","type":"journal-article","created":{"date-parts":[[2025,3,22]],"date-time":"2025-03-22T18:53:46Z","timestamp":1742669626000},"page":"2741-2760","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Binary stretch embedding of weighted graphs"],"prefix":"10.1007","volume":"93","author":[{"given":"Javad","family":"Ebrahimi Boroojeni","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mehri","family":"Oghbaei Bonab","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,21]]},"reference":[{"key":"1608_CR1","doi-asserted-by":"crossref","unstructured":"Astola H., Tabus I.: Bounds on the size of Lee-codes. In: 8th International Symposium on Image and Signal Processing and Analysis (ISPA), pp. 471\u2013476. IEEE, Trieste (2013).","DOI":"10.1109\/ISPA.2013.6703787"},{"issue":"1","key":"1608_CR2","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1186\/s40064-016-1863-8","volume":"5","author":"H Astola","year":"2016","unstructured":"Astola H., Tabus I.: On the linear programming bound for linear Lee codes. Springerplus 5(1), 246 (2016).","journal-title":"Springerplus"},{"key":"1608_CR3","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1090\/conm\/453\/08795","volume":"453","author":"H Bandelt","year":"2008","unstructured":"Bandelt H., Chepoi V.: Metric graph theory and geometry: a survey. Contemp. Math. 453, 49\u201386 (2008).","journal-title":"Contemp. Math."},{"key":"1608_CR4","first-page":"1","volume-title":"29th International Conference on DNA Computing and Molecular Programming","author":"JD Berleant","year":"2023","unstructured":"Berleant J.D.: Rational design of DNA sequences with non-orthogonal binding interactions. In: Chen H., Evans C.G. (eds.) 29th International Conference on DNA Computing and Molecular Programming, pp. 1\u201322. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik, Dagstuhl (2023)."},{"key":"1608_CR5","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.dam.2023.02.005","volume":"332","author":"JD Berleant","year":"2023","unstructured":"Berleant J.D., Sheridan K., Condon A., Williams V.V., Bathe M.: Isometric Hamming embeddings of weighted graphs. Discret. Appl. Math. 332, 119\u2013128 (2023).","journal-title":"Discret. Appl. Math."},{"key":"1608_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5","volume-title":"Graph Theory","author":"JA Bondy","year":"2008","unstructured":"Bondy J.A., Murty U.S.: Graph Theory. Springer, London (2008)."},{"key":"1608_CR7","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1007\/BF02776078","volume":"52","author":"J Bourgain","year":"1985","unstructured":"Bourgain J.: On Lipschitz embedding of finite metric spaces in Hilbert space. Isr. J. Math. 52, 46\u201352 (1985).","journal-title":"Isr. J. Math."},{"issue":"2\u20133","key":"1608_CR8","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1006\/eujc.1996.0024","volume":"17","author":"MM Deza","year":"1996","unstructured":"Deza M.M., Shpectorov S.V.: Recognition of the $$l_1$$-graphs with complexity $$o(nm)$$, or football in a hypercube. Eur. J. Comb. 17(2\u20133), 279\u2013289 (1996).","journal-title":"Eur. J. Comb."},{"key":"1608_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04295-9","volume-title":"Geometry of Cuts and Metrics","author":"MM Deza","year":"1997","unstructured":"Deza M.M., Laurent M., Weismantel R.: Geometry of Cuts and Metrics. Springer, Heidelberg (1997)."},{"issue":"3","key":"1608_CR10","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/0095-8956(73)90010-5","volume":"14","author":"D\u017d Djokovi\u0107","year":"1973","unstructured":"Djokovi\u0107 D.\u017d: Distance-preserving subgraphs of hypercubes. J. Comb. Theory Ser. B 14(3), 263\u2013267 (1973).","journal-title":"J. Comb. Theory Ser. B"},{"key":"1608_CR11","doi-asserted-by":"crossref","unstructured":"Fekete M.: \u00dcber die verteilung der wurzeln bei gewissen algebraischen gleichungen mit ganzzahligen koeffizienten. Math. Z. 228\u2013249 (1923).","DOI":"10.1007\/BF01504345"},{"issue":"6","key":"1608_CR12","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1007\/BF01074705","volume":"1","author":"VV Firsov","year":"1965","unstructured":"Firsov V.V.: Isometric embedding of a graph in a Boolean cube. Cybern. Syst. Anal. 1(6), 112\u2013113 (1965).","journal-title":"Cybern. Syst. Anal."},{"issue":"8","key":"1608_CR13","doi-asserted-by":"publisher","first-page":"4982","DOI":"10.1109\/TIT.2017.2700847","volume":"63","author":"R Gabrys","year":"2017","unstructured":"Gabrys R., Kiah H.M., Milenkovic O.: Asymmetric Lee distance codes for DNA-based storage. IEEE Trans. Inf. Theory 63(8), 4982\u20134995 (2017).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"1608_CR14","doi-asserted-by":"publisher","first-page":"2495","DOI":"10.1002\/j.1538-7305.1971.tb02618.x","volume":"50","author":"RL Graham","year":"1971","unstructured":"Graham R.L., Pollak H.O.: On the addressing problem for loop switching. Bell Syst. Tech. J. 50(8), 2495\u20132519 (1971).","journal-title":"Bell Syst. Tech. J."},{"key":"1608_CR15","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/BFb0067362","volume-title":"Graph Theory and Applications","author":"RL Graham","year":"1972","unstructured":"Graham R.L., Pollak H.O.: On embedding graphs in squashed cubes. In: Alavi Y., Lick D.R., White A.T. (eds.) Graph Theory and Applications, pp. 99\u2013110. Springer, Heidelberg (1972)."},{"issue":"2","key":"1608_CR16","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1090\/S0002-9947-1985-0776391-5","volume":"288","author":"RL Graham","year":"1985","unstructured":"Graham R.L., Winkler P.M.: On isometric embeddings of graphs. Trans. Am. Math. Soc. 288(2), 527\u2013536 (1985).","journal-title":"Trans. Am. Math. Soc."},{"issue":"2","key":"1608_CR17","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1006\/jcta.2000.3083","volume":"93","author":"AJ Hoffman","year":"2001","unstructured":"Hoffman A.J.: On a problem of Zaks. J. Comb. Theory Ser. A 93(2), 371\u2013377 (2001).","journal-title":"J. Comb. Theory Ser. A"},{"key":"1608_CR18","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1109\/TEC.1958.5222529","volume":"2","author":"WH Kautz","year":"1958","unstructured":"Kautz W.H.: Unit-distance error-checking codes. IRE Trans. Electron. Comput. 2, 179\u2013180 (1958).","journal-title":"IRE Trans. Electron. Comput."},{"issue":"2","key":"1608_CR19","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1109\/TIT.1958.1057446","volume":"4","author":"C Lee","year":"1958","unstructured":"Lee C.: Some properties of nonbinary error-correcting codes. IRE Trans. Inf. Theory 4(2), 77\u201382 (1958).","journal-title":"IRE Trans. Inf. Theory"},{"key":"1608_CR20","doi-asserted-by":"publisher","first-page":"357","DOI":"10.7717\/peerj-cs.357","volume":"7","author":"I Makarov","year":"2021","unstructured":"Makarov I., Kiselev D., Nikitinsky N., Subelj L.: Survey on graph embeddings and their applications to machine learning problems on graphs. PeerJ Comput. Sci. 7, 357 (2021).","journal-title":"PeerJ Comput. Sci."},{"key":"1608_CR21","unstructured":"Matou\u0161ek J.: Lecture Notes on Metric Embeddings. Technical Report, ETH Z\u00fcrich (2013)."},{"key":"1608_CR22","volume-title":"Understanding and Using Linear Programming","author":"J Matousek","year":"2007","unstructured":"Matousek J., Gartner B.: Understanding and Using Linear Programming. Springer, Heidelberg (2007)."},{"issue":"9","key":"1608_CR23","doi-asserted-by":"publisher","first-page":"2579","DOI":"10.1016\/j.disc.2019.05.019","volume":"342","author":"SC Polak","year":"2019","unstructured":"Polak S.C.: Semidefinite programming bounds for Lee codes. Discret. Math. 342(9), 2579\u20132589 (2019).","journal-title":"Discret. Math."},{"key":"1608_CR24","first-page":"150","volume-title":"International Workshop on Graph-Theoretic Concepts in Computer Science","author":"AL Rosenberg","year":"1980","unstructured":"Rosenberg A.L.: Issues in the study of graph embeddings. In: Noltemeier H. (ed.) International Workshop on Graph-Theoretic Concepts in Computer Science, pp. 150\u2013176. Springer, Heidelberg (1980)."},{"issue":"2","key":"1608_CR25","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1006\/eujc.1993.1016","volume":"14","author":"SV Shpectorov","year":"1993","unstructured":"Shpectorov S.V.: On scale embeddings of graphs into hypercubes. Eur. J. Comb. 14(2), 117\u2013130 (1993).","journal-title":"Eur. J. Comb."},{"key":"1608_CR26","volume-title":"Introduction to Coding Theory","author":"JH Van Lint","year":"1998","unstructured":"Van Lint J.H.: Introduction to Coding Theory. Springer, Berlin (1998)."},{"issue":"2","key":"1608_CR27","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0095-8956(90)90073-9","volume":"50","author":"E Wilkeit","year":"1990","unstructured":"Wilkeit E.: Isometric embeddings in Hamming graphs. J. Comb. Theory Ser. B 50(2), 179\u2013197 (1990).","journal-title":"J. Comb. Theory Ser. B"},{"issue":"2","key":"1608_CR28","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1016\/0166-218X(84)90069-6","volume":"7","author":"PM Winkler","year":"1984","unstructured":"Winkler P.M.: Isometric embedding in products of complete graphs. Discret. Appl. Math. 7(2), 221\u2013225 (1984).","journal-title":"Discret. Appl. Math."},{"issue":"2","key":"1608_CR29","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/0097-3165(88)90001-5","volume":"48","author":"J Zaks","year":"1988","unstructured":"Zaks J.: Nearly-neighborly families of tetrahedra and the decomposition of some multigraphs. J. Comb. Theory Ser. A 48(2), 147\u2013155 (1988).","journal-title":"J. Comb. Theory Ser. A"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01608-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-025-01608-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01608-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T07:55:46Z","timestamp":1757145346000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-025-01608-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,21]]},"references-count":29,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["1608"],"URL":"https:\/\/doi.org\/10.1007\/s10623-025-01608-w","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[2025,3,21]]},"assertion":[{"value":"13 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 August 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}