{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T08:47:05Z","timestamp":1767948425609,"version":"3.49.0"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T00:00:00Z","timestamp":1720396800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T00:00:00Z","timestamp":1720396800000},"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":["AAECC"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s00200-024-00666-2","type":"journal-article","created":{"date-parts":[[2024,7,7]],"date-time":"2024-07-07T23:13:03Z","timestamp":1720393983000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Algebraic lattices coming from $${\\mathbb {Z}}$$-modules generalizing ramified prime ideals in odd prime degree cyclic number fields"],"prefix":"10.1007","volume":"37","author":[{"given":"Antonio Aparecido","family":"de Andrade","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robson Ricardo","family":"de Araujo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Trajano Pires","family":"da Nobrega Neto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jefferson Luiz Rocha","family":"Bastos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,8]]},"reference":[{"key":"666_CR1","volume-title":"Sphere-Packings, Lattices, and Groups","author":"JH Conway","year":"1987","unstructured":"Conway, J.H., Sloane, N.J.A., Bannai, E.: Sphere-Packings, Lattices, and Groups. Springer, New York (1987)"},{"key":"666_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-67882-5","volume-title":"Lattices Applied to Coding for Reliable and Secure Communications","author":"SIR Costa","year":"2017","unstructured":"Costa, S.I.R., Oggier, F., Campello, A., Belfiore, J.-C., Viterbo, E.: Lattices Applied to Coding for Reliable and Secure Communications, vol. VI. Springer, New York (2017)"},{"key":"666_CR3","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1090\/conm\/241\/03628","volume":"241","author":"E Bayer-Fluckiger","year":"1999","unstructured":"Bayer-Fluckiger, E.: Lattices and number fields. Contemp. Math. 241, 69\u201374 (1999)","journal-title":"Contemp. Math."},{"key":"666_CR4","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1590\/S1807-03022010000300010","volume":"29","author":"AA Andrade","year":"2010","unstructured":"Andrade, A.A., Ferrari, A.J., Benedito, C.W.O., Costa, S.I.R.: Constructions of algebraic lattices. Comput. Appl. Math. 29, 493\u2013505 (2010). https:\/\/doi.org\/10.1590\/S1807-03022010000300010","journal-title":"Comput. Appl. Math."},{"key":"666_CR5","doi-asserted-by":"publisher","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: On Ideal Lattices and Learning With Errors Over Rings In: Advances in Cryptology\u2014EUROCRYPT 2010, pp. 1\u2013 23. Springer, Berlin ( 2010). https:\/\/doi.org\/10.1007\/978-3-642-13190-5_1","DOI":"10.1007\/978-3-642-13190-5_1"},{"key":"666_CR6","doi-asserted-by":"publisher","first-page":"2397","DOI":"10.1016\/j.jnt.2012.05.002","volume":"132","author":"GC Jorge","year":"2011","unstructured":"Jorge, G.C., Ferrari, A.J., Costa, S.I.R.: Rotated Dn-lattices. J. Number Theory 132, 2397\u20132406 (2011). https:\/\/doi.org\/10.1016\/j.jnt.2012.05.002","journal-title":"J. Number Theory"},{"key":"666_CR7","doi-asserted-by":"publisher","unstructured":"Jorge, G.C., Andrade, A.A., Costa, S.I.R., Eloir Strapasson. J.: Algebraic constructions of densest lattices. Journal of Algebra 429, 218\u2013235 (2015). https:\/\/doi.org\/10.1016\/j.jalgebra.2014.12.044","DOI":"10.1016\/j.jalgebra.2014.12.044"},{"issue":"01","key":"666_CR8","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1142\/S179304211250011X","volume":"08","author":"L Fukshansky","year":"2012","unstructured":"Fukshansky, L., Petersen, K.: On well-rounded ideal lattices. Int. J. Number Theory 08(01), 189\u2013206 (2012). https:\/\/doi.org\/10.1142\/S179304211250011X","journal-title":"Int. J. Number Theory"},{"key":"666_CR9","doi-asserted-by":"publisher","DOI":"10.1216\/rmj.2020.50.1137","author":"RR Araujo","year":"2017","unstructured":"Araujo, R.R., Jorge, G.C.: Construction of full diversity Dn-lattices for all n. Rocky Mt. J. Math. (2017). https:\/\/doi.org\/10.1216\/rmj.2020.50.1137","journal-title":"Rocky Mt. J. Math."},{"issue":"2","key":"666_CR10","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1109\/18.485720","volume":"42","author":"J Boutros","year":"1996","unstructured":"Boutros, J., Viterbo, E., Ratello, C., Belfiori, J.C.: Good lattice constellations for both Rayleigh fading and gaussian channels. IEEE Trans. Inform. Theory 42(2), 502\u2013518 (1996). https:\/\/doi.org\/10.1109\/18.485720","journal-title":"IEEE Trans. Inform. Theory"},{"key":"666_CR11","doi-asserted-by":"publisher","first-page":"1453","DOI":"10.1109\/18.681321","volume":"44","author":"J Boutros","year":"1998","unstructured":"Boutros, J., Viterbo, E.: Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel. IEEE Trans. Inf. Theory 44, 1453\u20131467 (1998). https:\/\/doi.org\/10.1109\/18.681321","journal-title":"IEEE Trans. Inf. Theory"},{"key":"666_CR12","doi-asserted-by":"publisher","DOI":"10.1561\/0100000003","author":"F Oggier","year":"2004","unstructured":"Oggier, F., Viterbo, E.: Algebraic number theory and code design for Rayleigh fading channels. Found. Trends Commun. Inform. Theory (2004). https:\/\/doi.org\/10.1561\/0100000003","journal-title":"Found. Trends Commun. Inform. Theory"},{"issue":"4","key":"666_CR13","doi-asserted-by":"publisher","first-page":"702","DOI":"10.1109\/TIT.2004.825045","volume":"50","author":"E Bayer-Fluckiger","year":"2004","unstructured":"Bayer-Fluckiger, E., Oggier, F., Viterbo, E.: New algebraic constructions of rotated z\/sup n\/-lattice constellations for the Rayleigh fading channel. IEEE Trans. Inf. Theory 50(4), 702\u2013714 (2004). https:\/\/doi.org\/10.1109\/TIT.2004.825045","journal-title":"IEEE Trans. Inf. Theory"},{"key":"666_CR14","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1109\/TWC.2008.060782","volume":"7","author":"AG F\u00e0bregas","year":"2008","unstructured":"F\u00e0bregas, A.G., Viterbo, E.: Sphere lower bound for rotated lattice constellations in fading channels. Wirel. Commun. IEEE Trans. 7, 825\u2013830 (2008). https:\/\/doi.org\/10.1109\/TWC.2008.060782","journal-title":"Wirel. Commun. IEEE Trans."},{"issue":"3","key":"666_CR15","doi-asserted-by":"publisher","first-page":"1099","DOI":"10.1109\/TCOMM.2013.011613.120069","volume":"61","author":"KN Pappi","year":"2013","unstructured":"Pappi, K.N., Chatzidiamantis, N.D., Karagiannidis, G.K.: Error performance of multidimensional lattice constellations-part ii: evaluation over fading channels. IEEE Trans. Commun. 61(3), 1099\u20131110 (2013). https:\/\/doi.org\/10.1109\/TCOMM.2013.011613.120069","journal-title":"IEEE Trans. Commun."},{"key":"666_CR16","doi-asserted-by":"publisher","unstructured":"Punekar, M., Boutros, J.J., Biglieri, E.: A poltyrev outage limit for lattices. In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 456\u2013 460 ( 2015). https:\/\/doi.org\/10.1109\/ISIT.2015.7282496","DOI":"10.1109\/ISIT.2015.7282496"},{"key":"666_CR17","doi-asserted-by":"publisher","unstructured":"Punekar, M., Boutros, J.J.: Diversity of Low-Density Lattices (2016). https:\/\/doi.org\/10.48550\/arXiv.1605.04128","DOI":"10.48550\/arXiv.1605.04128"},{"issue":"7","key":"666_CR18","doi-asserted-by":"publisher","first-page":"4104","DOI":"10.1109\/TCOMM.2020.2986203","volume":"68","author":"JC In\u00e1cio","year":"2020","unstructured":"In\u00e1cio, J.C., Uch\u00f4a-Filho, B.F., Ruyet, D.L., Montejo-S\u00e1nchez, S.: Full diversity multidimensional codebook design for fading channels: the combinatorial approach. IEEE Trans. Commun. 68(7), 4104\u20134116 (2020). https:\/\/doi.org\/10.1109\/TCOMM.2020.2986203","journal-title":"IEEE Trans. Commun."},{"issue":"5","key":"666_CR19","doi-asserted-by":"publisher","first-page":"2273","DOI":"10.1109\/TIT.2015.2416340","volume":"61","author":"W Kositwattanarerk","year":"2015","unstructured":"Kositwattanarerk, W., Ong, S.S., Oggier, F.: Construction a of lattices over number fields and block fading (wiretap) coding. IEEE Trans. Inf. Theory 61(5), 2273\u20132282 (2015). https:\/\/doi.org\/10.1109\/TIT.2015.2416340","journal-title":"IEEE Trans. Inf. Theory"},{"key":"666_CR20","doi-asserted-by":"publisher","unstructured":"Boutros, J.J., Belfiori, J.-C.: Construction-a full-diversity lattices. 2016, 9th International Symposium on Turbo Codes and Iterative Informations (ISTC) ( 2016) https:\/\/doi.org\/10.1109\/ISTC.2016.7593126","DOI":"10.1109\/ISTC.2016.7593126"},{"issue":"1","key":"666_CR21","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1109\/TIT.2020.3008973","volume":"67","author":"H Khodaiemehr","year":"2021","unstructured":"Khodaiemehr, H., Panario, D., Sadeghi, M.-R.: Design and practical decoding of full-diversity construction a lattices for block-fading channels. IEEE Trans. Inf. Theory 67(1), 138\u2013163 (2021). https:\/\/doi.org\/10.1109\/TIT.2020.3008973","journal-title":"IEEE Trans. Inf. Theory"},{"key":"666_CR22","doi-asserted-by":"publisher","unstructured":"Vehkalahti, R., Luzzi, L.: Number field lattices achieve gaussian and rayleigh channel capacity within a constant gap. In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 436\u2013 440 ( 2015). https:\/\/doi.org\/10.1109\/ISIT.2015.7282492","DOI":"10.1109\/ISIT.2015.7282492"},{"issue":"4","key":"666_CR23","doi-asserted-by":"publisher","first-page":"1075","DOI":"10.1216\/RMJ-2017-47-4-1075","volume":"47","author":"E.L Oliveira","year":"2017","unstructured":"Oliveira, E..L., Interlando, J..C., N\u00f3brega\u00a0Neto, T..P., Lopes, J..O..D.: The integral trace form of cyclic extensions of odd prime degree. Rocky Mt. J. Math. 47(4), 1075\u20131088 (2017). https:\/\/doi.org\/10.1216\/RMJ-2017-47-4-1075","journal-title":"Rocky Mt. J. Math."},{"issue":"2","key":"666_CR24","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s00013-018-1232-7","volume":"112","author":"RR Araujo","year":"2019","unstructured":"Araujo, R.R., Costa, S.I.R.: Well-rounded algebraic lattices in odd prime dimension. Arch. Math. 112(2), 139\u2013148 (2019). https:\/\/doi.org\/10.1007\/s00013-018-1232-7","journal-title":"Arch. Math."},{"issue":"4","key":"666_CR25","doi-asserted-by":"publisher","first-page":"2050080","DOI":"10.1142\/S0219498820500802","volume":"19","author":"R.R Araujo","year":"2020","unstructured":"Araujo, R..R., Chagas, A..C..M..M., Andrade, A..A., N\u00f3brega\u00a0Neto, T..P.: Trace form associated to cyclic number fields of ramified odd prime degree. J. Algebra Appl. 19(4), 2050080 (2020). https:\/\/doi.org\/10.1142\/S0219498820500802","journal-title":"J. Algebra Appl."},{"issue":"6","key":"666_CR26","first-page":"1009","volume":"33","author":"JC Interlando","year":"2020","unstructured":"Interlando, J.C., Andrade, A.A., Malaxechebarr\u00eda, B.G., Araujo, R.R.: Fully-diverse lattices from ramified cyclic extensions of prime degree. Int. J. Appl. Math. 33(6), 1009\u20131015 (2020)","journal-title":"Int. J. Appl. Math."},{"key":"666_CR27","unstructured":"Nebe, G., Sloane, N.J.A.: Table of Densest Packings Presently Known. www.math.rwth-aachen.de\/~Gabriele.Nebe\/LATTICES\/density.html. Accessed: 07\/13\/2023 (2012)"},{"issue":"10","key":"666_CR28","doi-asserted-by":"publisher","first-page":"1750186","DOI":"10.1142\/S0219498817501869","volume":"16","author":"J.V.L Nunes","year":"2017","unstructured":"Nunes, J..V..L., Interlando, J..C., N\u00f3brega\u00a0Neto, T..P., Lopes, J..O..D.: New p-dimensional lattices from cyclic extensions. J. Algebra Appl. 16(10), 1750186 (2017). https:\/\/doi.org\/10.1142\/S0219498817501869","journal-title":"J. Algebra Appl."},{"key":"666_CR29","doi-asserted-by":"publisher","unstructured":"Tran, D.T., Le, N.H., Tran, H.T.N.: Well-Rounded ideal lattices of cyclic cubic and quartic fields. Commun. Math. 31(2) (2023). https:\/\/doi.org\/10.46298\/cm.11138","DOI":"10.46298\/cm.11138"},{"key":"666_CR30","volume-title":"Algebraic Theory of Numbers","author":"P Samuel","year":"1982","unstructured":"Samuel, P.: Algebraic Theory of Numbers. Hermann, Paris (1982)"},{"key":"666_CR31","volume-title":"Introduction to Cyclotomic Fields","author":"L Washington","year":"1995","unstructured":"Washington, L.: Introduction to Cyclotomic Fields. Springer, New York (1995)"},{"issue":"1","key":"666_CR32","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1142\/S0219498806001636","volume":"5","author":"J.C Interlando","year":"2006","unstructured":"Interlando, J..C., Lopes, J..O..D., N\u00f3brega\u00a0Neto, T..P.: The discriminant of Abelian number fields. J. Algebra Appl. 5(1), 35\u201341 (2006). https:\/\/doi.org\/10.1142\/S0219498806001636","journal-title":"J. Algebra Appl."},{"issue":"3","key":"666_CR33","doi-asserted-by":"publisher","first-page":"1101","DOI":"10.1216\/rmjm\/1181069946","volume":"33","author":"BK Spearman","year":"2003","unstructured":"Spearman, B.K., Williams, K.S.: The discriminant of a cyclic field of odd prime degree. Rocky Mt. J. Math. 33(3), 1101\u20131122 (2003). https:\/\/doi.org\/10.1216\/rmjm\/1181069946","journal-title":"Rocky Mt. J. Math."},{"issue":"04","key":"666_CR34","doi-asserted-by":"publisher","first-page":"1550045","DOI":"10.1142\/S0219498815500450","volume":"14","author":"J.C Interlando","year":"2015","unstructured":"Interlando, J..C., N\u00f3brega\u00a0Neto, T..P., Rodrigues, T..M., Lopes, J..O..D.: A note on the integral trace form in cyclotomic fields. J. Algebra Appl. 14(04), 1550045 (2015). https:\/\/doi.org\/10.1142\/S0219498815500450","journal-title":"J. Algebra Appl."}],"container-title":["Applicable Algebra in Engineering, Communication and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-024-00666-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00200-024-00666-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00200-024-00666-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T07:14:34Z","timestamp":1767942874000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00200-024-00666-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,8]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["666"],"URL":"https:\/\/doi.org\/10.1007\/s00200-024-00666-2","relation":{},"ISSN":["0938-1279","1432-0622"],"issn-type":[{"value":"0938-1279","type":"print"},{"value":"1432-0622","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,8]]},"assertion":[{"value":"28 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 June 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 June 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 July 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no Conflict of interest and that they have no financial or nonfinancial interests that are directly or indirectly related to this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}