{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T04:41:06Z","timestamp":1767847266588,"version":"3.49.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T00:00:00Z","timestamp":1686614400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T00:00:00Z","timestamp":1686614400000},"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":["Combinatorica"],"published-print":{"date-parts":[[2023,8]]},"DOI":"10.1007\/s00493-023-00030-x","type":"journal-article","created":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T09:01:51Z","timestamp":1686646911000},"page":"681-716","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Large Family of Maximum Scattered Linear Sets of $${{\\,\\mathrm{{PG}}\\,}}(1,q^n)$$ and Their Associated MRD Codes"],"prefix":"10.1007","volume":"43","author":[{"given":"G.","family":"Longobardi","sequence":"first","affiliation":[]},{"given":"Giuseppe","family":"Marino","sequence":"additional","affiliation":[]},{"given":"Rocco","family":"Trombetti","sequence":"additional","affiliation":[]},{"given":"Yue","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,13]]},"reference":[{"issue":"2","key":"30_CR1","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s00493-016-3531-6","volume":"38","author":"D Bartoli","year":"2018","unstructured":"Bartoli, D., Giulietti, M., Marino, G., Polverino, O.: Maximum scattered linear sets and complete caps in Galois spaces. Combinatorica 38(2), 255\u2013278 (2018)","journal-title":"Combinatorica"},{"key":"30_CR2","unstructured":"Bartoli, D., Giulietti, M., Zini, G.: Towards the classification of exceptional scattered polynomials. arXiv:2206.13795"},{"key":"30_CR3","doi-asserted-by":"publisher","first-page":"105386","DOI":"10.1016\/j.jcta.2020.105386","volume":"179","author":"D Bartoli","year":"2021","unstructured":"Bartoli, D., Montanucci, M.: On the classification of exceptional scattered polynomials. J. Comb. Theory Ser. A 179, 105386 (2021)","journal-title":"J. Comb. Theory Ser. A"},{"issue":"1","key":"30_CR4","doi-asserted-by":"publisher","first-page":"125","DOI":"10.26493\/1855-3974.2137.7fa","volume":"19","author":"D Bartoli","year":"2020","unstructured":"Bartoli, D., Zanella, C., Zullo, F.: A new family of maximum scattered linear sets in $$\\rm PG (1, q^6)$$. Ars Math. Contemp. 19(1), 125\u2013145 (2020)","journal-title":"Ars Math. Contemp."},{"key":"30_CR5","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1016\/j.jalgebra.2018.03.010","volume":"509","author":"D Bartoli","year":"2018","unstructured":"Bartoli, D., Zhou, Y.: Exceptional scattered polynomials. J. Algebra 509, 507\u2013534 (2018)","journal-title":"J. Algebra"},{"issue":"1","key":"30_CR6","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1023\/A:1005283806897","volume":"81","author":"A Blokhuis","year":"2000","unstructured":"Blokhuis, A., Lavrauw, M.: Scattered spaces with respect to a spread in $$\\rm PG (n, q)$$. Geom. Dedic. 81(1), 231\u2013243 (2000)","journal-title":"Geom. Dedic."},{"key":"30_CR7","unstructured":"Couvreur, A., Debris-Alazard, T., Gaborit, P.: On the hardness of code equivalence problems in rank metric. [cs, math]. arXiv:2011.04611 (2020)"},{"key":"30_CR8","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1016\/j.jcta.2018.03.007","volume":"157","author":"B Csajb\u00f3k","year":"2018","unstructured":"Csajb\u00f3k, B., Marino, G., Polverino, O.: Classes and equivalence of linear sets in $$\\rm PG (1, q^n)$$. J. Comb. Theory Ser. A 157, 402\u2013426 (2018)","journal-title":"J. Comb. Theory Ser. A"},{"key":"30_CR9","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/j.laa.2018.02.027","volume":"548","author":"B Csajb\u00f3k","year":"2018","unstructured":"Csajb\u00f3k, B., Marino, G., Polverino, O., Zanella, C.: A new family of MRD-codes. Linear Algebra Appl. 548, 203\u2013220 (2018)","journal-title":"Linear Algebra Appl."},{"key":"30_CR10","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/j.ffa.2018.08.001","volume":"54","author":"B Csajb\u00f3k","year":"2018","unstructured":"Csajb\u00f3k, B., Marino, G., Zullo, F.: New maximum scattered linear sets of the projective line. Finite Fields Appl. 54, 133\u2013150 (2018)","journal-title":"Finite Fields Appl."},{"issue":"2","key":"30_CR11","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/s10623-015-0141-z","volume":"81","author":"B Csajb\u00f3k","year":"2016","unstructured":"Csajb\u00f3k, B., Zanella, C.: On the equivalence of linear sets. Des. Codes Cryptogr. 81(2), 269\u2013281 (2016)","journal-title":"Des. Codes Cryptogr."},{"key":"30_CR12","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1016\/0097-3165(78)90015-8","volume":"25","author":"P Delsarte","year":"1978","unstructured":"Delsarte, P.: Bilinear forms over the finite field, with applications to coding theory. J. Comb. Theory Ser. A 25, 226\u2013241 (1978)","journal-title":"J. Comb. Theory Ser. A"},{"key":"30_CR13","doi-asserted-by":"publisher","first-page":"691","DOI":"10.1016\/j.jalgebra.2020.09.034","volume":"565","author":"A Ferraguti","year":"2021","unstructured":"Ferraguti, A., Micheli, G.: Exceptional scatteredness in prime degree. J. Algebra 565, 691\u2013701 (2021)","journal-title":"J. Algebra"},{"key":"30_CR14","doi-asserted-by":"crossref","unstructured":"Gupta, S., Longobardi, G., Trombetti, R.: On the equivalence issue of a class of 2-dimensional linear Maximum Rank Distance codes. Preprint at arXiv: 2208.09701 (2022)","DOI":"10.1016\/j.laa.2023.08.012"},{"key":"30_CR15","volume-title":"Current Research Topics in Galois Geometry","author":"M Lavrauw","year":"2011","unstructured":"Lavrauw, M., Polverino, O.: Finite semifields and Galois geometry, chapter. In: De Beule, J., Storme, L. (eds.) Current Research Topics in Galois Geometry. NOVA Academic Publishers, Hauppauge (2011)"},{"key":"30_CR16","first-page":"271","volume-title":"Contemporary Mathematics","author":"M Lavrauw","year":"2015","unstructured":"Lavrauw, M., Van de Voorde, G.: Field reduction and linear sets in finite geometry. In: Kyureghyan, G., Mullen, G., Pott, A. (eds.) Contemporary Mathematics, vol. 632, pp. 271\u2013293. American Mathematical Society, Providence (2015)"},{"issue":"4","key":"30_CR17","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s00013-016-0949-4","volume":"107","author":"D Liebhold","year":"2016","unstructured":"Liebhold, D., Nebe, G.: Automorphism groups of Gabidulin-like codes. Arch. Math. 107(4), 355\u2013366 (2016)","journal-title":"Arch. Math."},{"issue":"3","key":"30_CR18","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1007\/s10801-020-01011-9","volume":"53","author":"G Longobardi","year":"2021","unstructured":"Longobardi, G., Zanella, C.: Linear sets and MRD-codes arising from a class of scattered linearized polynomials. J. Algebr. Comb. 53(3), 639\u2013661 (2021)","journal-title":"J. Algebr. Comb."},{"issue":"3","key":"30_CR19","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1023\/A:1005052007006","volume":"75","author":"G Lunardon","year":"1999","unstructured":"Lunardon, G.: Normal spreads. Geom. Dedic. 75(3), 245\u2013261 (1999)","journal-title":"Geom. Dedic."},{"issue":"1","key":"30_CR20","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1023\/A:1011265919847","volume":"14","author":"G Lunardon","year":"2001","unstructured":"Lunardon, G., Polverino, O.: Blocking sets and derivable partial spreads. J. Algebr. Comb. 14(1), 49\u201356 (2001)","journal-title":"J. Algebr. Comb."},{"issue":"2","key":"30_CR21","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/s10801-017-0755-5","volume":"46","author":"G Lunardon","year":"2017","unstructured":"Lunardon, G., Trombetti, R., Zhou, Y.: On kernels and nuclei of rank metric codes. J. Algebr. Comb. 46(2), 313\u2013340 (2017)","journal-title":"J. Algebr. Comb."},{"key":"30_CR22","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.jcta.2018.05.004","volume":"159","author":"G Lunardon","year":"2018","unstructured":"Lunardon, G., Trombetti, R., Zhou, Y.: Generalized twisted Gabidulin codes. J. Comb. Theory Ser. A 159, 79\u2013106 (2018)","journal-title":"J. Comb. Theory Ser. A"},{"key":"30_CR23","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/j.laa.2020.01.004","volume":"591","author":"G Marino","year":"2020","unstructured":"Marino, G., Montanucci, M., Zullo, F.: MRD-codes arising from the trinomial $$x^q+x^{q^3}+cx^{q^5}\\in {\\mathbb{F} }_{q^6}[x]$$. Linear Algebra Appl. 591, 99\u2013114 (2020)","journal-title":"Linear Algebra Appl."},{"key":"30_CR24","doi-asserted-by":"publisher","first-page":"102045","DOI":"10.1016\/j.ffa.2022.102045","volume":"81","author":"A Neri","year":"2022","unstructured":"Neri, A., Santonastaso, P., Zullo, F.: Extending two families of maximum rank distance codes. Finite Fields Appl. 81, 102045 (2022)","journal-title":"Finite Fields Appl."},{"key":"30_CR25","doi-asserted-by":"publisher","first-page":"3096","DOI":"10.1016\/j.disc.2009.04.007","volume":"22","author":"O Polverino","year":"2010","unstructured":"Polverino, O.: Linear sets in finite projective spaces. Discret. Math. 22, 3096\u20133107 (2010)","journal-title":"Discret. Math."},{"key":"30_CR26","first-page":"46","volume":"89","author":"O Polverino","year":"2020","unstructured":"Polverino, O., Zullo, F.: Connections between scattered linear sets and MRD-codes. Bull. ICA 89, 46\u201374 (2020)","journal-title":"Bull. ICA"},{"issue":"3","key":"30_CR27","doi-asserted-by":"publisher","first-page":"475","DOI":"10.3934\/amc.2016019","volume":"10","author":"J Sheekey","year":"2016","unstructured":"Sheekey, J.: A new family of linear maximum rank distance codes. Adv. Math. Commun. 10(3), 475\u2013488 (2016)","journal-title":"Adv. Math. Commun."},{"key":"30_CR28","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1515\/9783110642094-013","volume-title":"Combinatorics and Finite Fields. Difference Sets, Polynomials, Pseudorandomness and Applications","author":"J Sheekey","year":"2019","unstructured":"Sheekey, J.: MRD codes: constructions and connections. In: Schmidt, K.-U., Winterhof, A. (eds.) Combinatorics and Finite Fields. Difference Sets, Polynomials, Pseudorandomness and Applications, pp. 255\u2013286. De Gruyter, Berlin (2019)"},{"key":"30_CR29","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1007\/s10623-019-00703-z","volume":"88","author":"J Sheekey","year":"2020","unstructured":"Sheekey, J., Van de Voorde, G.: Rank-metric codes, linear sets, and their duality. Des. Codes Cryptogr. 88, 655\u2013675 (2020)","journal-title":"Des. Codes Cryptogr."},{"issue":"5","key":"30_CR30","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2022.113313","volume":"346","author":"W Tang","year":"2023","unstructured":"Tang, W., Zhou, Y., Zullo, F.: On the automorphism groups of Lunardon\u2013Polverino scattered linear sets. Discret. Math. 346(5), 113313 (2023)","journal-title":"Discret. Math."},{"issue":"5","key":"30_CR31","doi-asserted-by":"publisher","first-page":"111800","DOI":"10.1016\/j.disc.2019.111800","volume":"343","author":"C Zanella","year":"2020","unstructured":"Zanella, C., Zullo, F.: Vertex properties of maximum scattered linear sets of $$\\rm PG (1, q^n)$$. Discret. Math. 343(5), 111800 (2020)","journal-title":"Discret. Math."}],"container-title":["Combinatorica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-023-00030-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00493-023-00030-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00493-023-00030-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:38:12Z","timestamp":1702600692000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00493-023-00030-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,13]]},"references-count":31,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["30"],"URL":"https:\/\/doi.org\/10.1007\/s00493-023-00030-x","relation":{},"ISSN":["0209-9683","1439-6912"],"issn-type":[{"value":"0209-9683","type":"print"},{"value":"1439-6912","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,13]]},"assertion":[{"value":"18 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 February 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 June 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}