TY - JOUR

T1 - Elements of high order in finite fields specified by binomials

AU - Bovdi, V.

AU - Diene, A.

AU - Popovych, R.

N1 - Funding Information:
Authors would like to express their gratitude to an anonymous referee for valuable remarks and his/her help in improving this article. The research was supported by the UAEU UPAR grant G00003431.
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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U2 - 10.15330/cmp.14.1.238-246

DO - 10.15330/cmp.14.1.238-246

M3 - Article

AN - SCOPUS:85134838608

SN - 2075-9827

VL - 14

SP - 238

EP - 246

JO - Carpathian Mathematical Publications

JF - Carpathian Mathematical Publications

IS - 1

ER -