Sufficient condition for existence of special type of primitive normal elements over finite fields

2019/02/13 by Hazarika, Himangshu, Basnet, Dhiren Kumar
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.04736

Abstract

Let \mathbbF_qⁿ be the extension of the field \mathbbF_q of degree n, where q is power of prime p, i.e q=p^k, where k is a positive integer. In this paper, we provide sufficient condition for the existence of a primitive normal element α∈\mathbbF_qⁿ such that α²+α+1 is also primitive normal element over \mathbbF_qⁿ.

Related

• A note on primitive 1-normal elements over finite fields
• About r- primitive and k-normal elements in finite fields
• Existence of primitive k-normal elements for critical values over finite fields
• On the existence of primitive completely normal bases of finite fields
• On k-normal elements over finite fields