{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T07:40:58Z","timestamp":1770277258553,"version":"3.49.0"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"Scientific and Industrial Research, New Delhi","award":["09\/796(0099)\/2019-EMR-I"],"award-info":[{"award-number":["09\/796(0099)\/2019-EMR-I"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,3]]},"abstract":"<jats:p> Let [Formula: see text] be an even prime power and [Formula: see text] an integer. By [Formula: see text], we denote the finite field of order [Formula: see text] and by [Formula: see text] its extension of degree [Formula: see text]. In this paper, we investigate the existence of a primitive normal pair [Formula: see text], with [Formula: see text] where the rank of the matrix [Formula: see text] is 2. Namely, we establish sufficient conditions to show that nearly all fields of even characteristic possess such elements, except for [Formula: see text] if [Formula: see text] and [Formula: see text] is odd, and then we provide an explicit small list of possible and genuine exceptional pairs [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196722500187","type":"journal-article","created":{"date-parts":[[2022,2,8]],"date-time":"2022-02-08T07:16:51Z","timestamp":1644304611000},"page":"357-382","source":"Crossref","is-referenced-by-count":4,"title":["On the existence of primitive normal elements of rational form over finite fields of even characteristic"],"prefix":"10.1142","volume":"32","author":[{"given":"Himangshu","family":"Hazarika","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Tezpur University, Assam 784028, India"}]},{"given":"Dhiren Kumar","family":"Basnet","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tezpur University, Assam 784028, India"}]},{"given":"Giorgos","family":"Kapetanakis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Thessaly, 3rd km Old National Road Lamia-Athens, 35100 Lamia, Greece"}]}],"member":"219","published-online":{"date-parts":[[2022,2,7]]},"reference":[{"key":"S0218196722500187BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3390"},{"key":"S0218196722500187BIB002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1952-0051869-9"},{"key":"S0218196722500187BIB003","doi-asserted-by":"publisher","DOI":"10.4064\/aa-94-2-173-201"},{"key":"S0218196722500187BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2014.01.012"},{"key":"S0218196722500187BIB005","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610702003782"},{"key":"S0218196722500187BIB006","doi-asserted-by":"publisher","DOI":"10.4064\/aa143-4-1"},{"key":"S0218196722500187BIB008","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/hau012"},{"key":"S0218196722500187BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2018.05.005"},{"key":"S0218196722500187BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-014-0230-7"},{"key":"S0218196722500187BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.ffa.2013.12.002"},{"key":"S0218196722500187BIB012","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1987-0866111-3"},{"key":"S0218196722500187BIB013","volume-title":"Finite Fields","author":"Lidl R.","year":"1997","edition":"2"},{"issue":"3","key":"S0218196722500187BIB014","first-page":"657","volume":"49","author":"Tian T.","year":"2006","journal-title":"Acta. Math. Sin. (Chin. Ser.)"},{"key":"S0218196722500187BIB015","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-97-00835-1"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196722500187","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,15]],"date-time":"2022-03-15T06:05:59Z","timestamp":1647324359000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196722500187"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,7]]},"references-count":14,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2022,3]]}},"alternative-id":["10.1142\/S0218196722500187"],"URL":"https:\/\/doi.org\/10.1142\/s0218196722500187","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,7]]}}}