{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:21:33Z","timestamp":1740122493290,"version":"3.37.3"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,3,12]],"date-time":"2023-03-12T00:00:00Z","timestamp":1678579200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,3,12]],"date-time":"2023-03-12T00:00:00Z","timestamp":1678579200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100004901","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Minas Gerais","doi-asserted-by":"publisher","award":["RED-00133-21","RED-00133-21","APQ-02546-21","APQ-00470-22"],"award-info":[{"award-number":["RED-00133-21","RED-00133-21","APQ-02546-21","APQ-00470-22"]}],"id":[{"id":"10.13039\/501100004901","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2023,6]]},"DOI":"10.1007\/s10623-023-01201-z","type":"journal-article","created":{"date-parts":[[2023,3,12]],"date-time":"2023-03-12T12:02:28Z","timestamp":1678622548000},"page":"2323-2346","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On arithmetic progressions in finite fields"],"prefix":"10.1007","volume":"91","author":[{"given":"Ab\u00edlio","family":"Lemos","sequence":"first","affiliation":[]},{"given":"Victor G. L.","family":"Neumann","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8632-4764","authenticated-orcid":false,"given":"S\u00e1vio","family":"Ribas","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,3,12]]},"reference":[{"key":"1201_CR1","doi-asserted-by":"publisher","first-page":"101864","DOI":"10.1016\/j.ffa.2021.101864","volume":"73","author":"JJR Aguirre","year":"2021","unstructured":"Aguirre J.J.R., Neumann V.G.L.: Existence of primitive $$2$$-normal elements in finite fields. Finite Fields Appl. 73, 101864 (2021).","journal-title":"Finite Fields Appl."},{"key":"1201_CR2","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1007\/s00574-021-00277-2","volume":"53","author":"C Carvalho","year":"2022","unstructured":"Carvalho C., Guardieiro J.P., Neumann V.G.L., Tizziotti G.: On the existence of pairs of primitive and normal elements over finite fields. Bull. Braz. Math. Soc. (N.S.) 53, 677\u2013699 (2022).","journal-title":"Bull. Braz. Math. Soc. (N.S.)"},{"key":"1201_CR3","doi-asserted-by":"crossref","unstructured":"Cohen S.D., Oliveira e Silva T., Trudgian T.: On consecutive primitive elements in a finite field. Bull. Lond. Math. Soc. 47(3), 418\u2013426 (2015).","DOI":"10.1112\/blms\/bdv018"},{"key":"1201_CR4","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1112\/S0025579300011050","volume":"32","author":"SD Cohen","year":"1985","unstructured":"Cohen S.D.: Pairs of primitive roots. Mathematika 32, 276\u2013285 (1985).","journal-title":"Mathematika"},{"issue":"1","key":"1201_CR5","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1112\/S0024610702003782","volume":"67","author":"SD Cohen","year":"2003","unstructured":"Cohen S.D., Huczynska S.: The primitive normal basis theorem without a computer. J. Lond. Math. Soc. 67(1), 41\u201356 (2003).","journal-title":"J. Lond. Math. Soc."},{"key":"1201_CR6","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1093\/qmath\/hau012","volume":"65","author":"L Fu","year":"2014","unstructured":"Fu L., Wan D.Q.: A class of incomplete character sums. Q. J. Math. 65, 1195\u20131211 (2014).","journal-title":"Q. J. Math."},{"key":"1201_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-60806-4","volume-title":"Topics in Galois Fields","author":"D Hachenberger","year":"2020","unstructured":"Hachenberger D., Jungnickel D.: Topics in Galois Fields. Springer, New York (2020)."},{"key":"1201_CR8","first-page":"1521","volume":"91","author":"T Jarso","year":"2022","unstructured":"Jarso T., Trudgian T.: Four consecutive primitive elements in a finite field. Math. Comp. 91, 1521\u20131532 (2022).","journal-title":"Math. Comp."},{"key":"1201_CR9","doi-asserted-by":"publisher","first-page":"1459","DOI":"10.1007\/s10623-018-0543-9","volume":"87","author":"G Kapetanakis","year":"2019","unstructured":"Kapetanakis G., Reis L.: Variations of the primitive normal basis theorem. Des. Codes Cryptogr. 87, 1459\u20131480 (2019).","journal-title":"Des. Codes Cryptogr."},{"key":"1201_CR10","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.ffa.2013.12.002","volume":"26","author":"G Kapetanakis","year":"2014","unstructured":"Kapetanakis G.: Normal bases and primitive elements over finite fields. Finite Fields Appl. 26, 123\u2013143 (2014).","journal-title":"Finite Fields Appl."},{"key":"1201_CR11","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1090\/S0025-5718-1987-0866111-3","volume":"48","author":"HW Lenstra","year":"1987","unstructured":"Lenstra H.W., Schoof R.: Primitive normal bases for finite fields. Math. Comp. 48, 217\u2013231 (1987).","journal-title":"Math. Comp."},{"key":"1201_CR12","volume-title":"Finite Fields","author":"R Lidl","year":"1997","unstructured":"Lidl R., Niederreiter H.: Finite Fields. Cambridge University Press, Cambridge (1997)."},{"issue":"1","key":"1201_CR13","first-page":"64","volume":"6","author":"JB Rosser","year":"1962","unstructured":"Rosser J.B., Schoenfeld L.: Approximate formulas for some functions of prime numbers. Ill. J. Math. 6(1), 64\u201394 (1962).","journal-title":"Ill. J. Math."},{"key":"1201_CR14","unstructured":"The Sage Developers, SageMath, the Sage Mathematics Software System (Version 8.1), https:\/\/www.sagemath.org (2020)."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-023-01201-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-023-01201-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-023-01201-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T16:13:14Z","timestamp":1685031194000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-023-01201-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,12]]},"references-count":14,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["1201"],"URL":"https:\/\/doi.org\/10.1007\/s10623-023-01201-z","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[2023,3,12]]},"assertion":[{"value":"8 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 December 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 February 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 March 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}