{"title":"基于环形多项式的有限域扩展中的正规高阶元","authors":"R. Popovych, Ruslan Skuratovskii","doi":"10.12958/adm1117","DOIUrl":null,"url":null,"abstract":"We consider elements which are both of high multiplicative order and normal in extensions \\(F_{q^{m} } \\) of the field \\(F_{q} \\). If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders.","PeriodicalId":44176,"journal":{"name":"Algebra & Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2020-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Normal high order elements in finite field extensions based on the cyclotomic polynomials\",\"authors\":\"R. Popovych, Ruslan Skuratovskii\",\"doi\":\"10.12958/adm1117\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider elements which are both of high multiplicative order and normal in extensions \\\\(F_{q^{m} } \\\\) of the field \\\\(F_{q} \\\\). If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders.\",\"PeriodicalId\":44176,\"journal\":{\"name\":\"Algebra & Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2020-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra & Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12958/adm1117\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra & Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12958/adm1117","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Normal high order elements in finite field extensions based on the cyclotomic polynomials
We consider elements which are both of high multiplicative order and normal in extensions \(F_{q^{m} } \) of the field \(F_{q} \). If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders.
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