Elements of high order in finite fields specified by binomials

V. Bovdi; A. Diene; R. Popovych

doi:10.15330/cmp.14.1.238-246

Elements of high order in finite fields specified by binomials

V. Bovdi
, A. Diene
, R. Popovych

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Let F_q be a field with q elements, where q is a power of a prime number p ≥ 5. For any integer m ≥ 2 and a ∈ F^∗q such that the polynomial x^m − a is irreducible in F_q [x], we combine two different methods to explicitly construct elements of high order in the field F_q [x]/〈x^m − a〉. Namely, we find elements with multiplicative order of at least 5^3√m/2, which is better than previously obtained bound for such family of extension fields.

Original language	English
Pages (from-to)	238-246
Number of pages	9
Journal	Carpathian Mathematical Publications
Volume	14
Issue number	1
DOIs	https://doi.org/10.15330/cmp.14.1.238-246
Publication status	Published - Jun 30 2022

Keywords

binomial
element of high multiplicative order
finite field
multiplicative order

ASJC Scopus subject areas

General Mathematics

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10.15330/cmp.14.1.238-246

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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 ∈ F∗q 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.",

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author = "V. Bovdi and A. Diene and R. Popovych",

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AU - Bovdi, V.

AU - Diene, A.

AU - Popovych, R.

N1 - Publisher Copyright: © Bovdi V., Diene A., Popovych R., 2022.

PY - 2022/6/30

Y1 - 2022/6/30

N2 - 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 ∈ F∗q 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.

AB - 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 ∈ F∗q 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.

KW - binomial

KW - element of high multiplicative order

KW - finite field

KW - multiplicative order

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M3 - Article

AN - SCOPUS:85134838608

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EP - 246

JO - Carpathian Mathematical Publications

JF - Carpathian Mathematical Publications

IS - 1

ER -

Elements of high order in finite fields specified by binomials

Abstract

Keywords

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