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 -