Elements of high order in finite fields specified by binomials

V. Bovdi, A. Diene, R. Popovych

Research output: Contribution to journalArticlepeer-review

Abstract

Let Fq be a field with q elements, where q is a power of a prime number p ≥ 5. For any integer m ≥ 2 and a ∈ Fq such that the polynomial xm − a is irreducible in Fq [x], we combine two different methods to explicitly construct elements of high order in the field Fq [x]/〈xm − a〉. Namely, we find elements with multiplicative order of at least 53√m/2, which is better than previously obtained bound for such family of extension fields.

Original languageEnglish
Pages (from-to)238-246
Number of pages9
JournalCarpathian Mathematical Publications
Volume14
Issue number1
DOIs
Publication statusPublished - Jun 30 2022

Keywords

  • binomial
  • element of high multiplicative order
  • finite field
  • multiplicative order

ASJC Scopus subject areas

  • General Mathematics

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