原始元素
数学
组合数学
有限域
整数(计算机科学)
要素(刑法)
乘法函数
主电源
原根模n
除数(代数几何)
素数(序理论)
订单(交换)
最小公倍数
互质整数
最大公约数
乘法群
本原多项式
离散数学
数学分析
计算机科学
经济
程序设计语言
法学
政治学
财务
作者
Mamta Rani,Ashok Sharma,Sharwan K. Tiwari
标识
DOI:10.1016/j.ffa.2022.102053
摘要
Let r, n be positive integers, k be a non-negative integer and q be any prime power such that r|qn−1. An element α of the finite field Fqn is called an r-primitive element, if its multiplicative order is (qn−1)/r and it is called a k-normal element over Fq, if the degree of the greatest common divisor of the polynomials mα(x)=∑i=1nαqi−1xn−i and xn−1 is k. In this article, we discuss the existence of an element α∈Fqn which is both r-primitive and k-normal over Fq. In particular, we show that there exists an element α∈Fqn, which is both 2-primitive and 2-normal over Fq if and only if q is an odd prime power and either n≥5 and gcd(q3−q,n)≠1 or n=4 and q≡1(mod4).
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