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Existence of rational primitive normal pairs over finite fields | ||
| International Journal of Group Theory | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 تیر 1401 اصل مقاله (421.54 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2022.133016.1784 | ||
| نویسندگان | ||
Rajendra Sharma   1؛ Soniya Takshak2؛ Ambrish Awasthi3؛ Hariom Sharma4
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| 1Indian Institute of Technology Delhi | ||
| 2Mathematics, Research Scholar, Indian Institute of Technology, Hauz Khas, Delhi | ||
| 3Scientific Analysis Group, Scientist, Defence Research & Development Organisation, Metcalfe House, Delhi | ||
| 4Mathematics, Assistant Professor, S.S. Govt. P.G. College, Tigaon, Faridabad, Haryana, India | ||
| چکیده | ||
| For a finite field F_{q^n} and a rational function f =f_1/f_2 ∈ F_{q^n} (x), we present a sufficient condition for the existence of a primitive normal element α ∈ F_{q^n} such that f(α) is also primitive in F_{q^n}, where f(x) is a rational function in F_{q^n}(x) of degree sum m (degree sum of f(x) = f_1(x)/f_2(x) is defined to be the sum of the degrees of f_1(x) and f_2(x)). Additionally, for rational functions of degree sum 4, we proved that there are only 37 and 16 exceptional values of (q, n) when q = 2^k and q = 3^k respectively. | ||
| کلیدواژه‌ها | ||
| Finite Field؛ Primitive Element؛ Normal Element؛ Character | ||
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آمار تعداد مشاهده مقاله: 106 تعداد دریافت فایل اصل مقاله: 4 |
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