H. Hazarika

activity

20192024

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

1 citations · 1 across the 7 of their papers we have counts for

collaborators

7 papers

math.NT2024

Existence of Special Types Primitive Pairs in Finite Fields Avoiding Affine Hyperplanes

Himangshu Hazarika, Giorgos Kapetanakis, Dhiren Kumar Basnet

Let $\Fm$ be finite fields of order $q^{m}$ , where $m \geq 2$ and $q$ , a prime power. Given $\F$-affine hyperplanes $A_{1}, \dots, A_{m}$ of $\Fm$ in general position, we study the existe…

math.NT2023

Primitive normal pairs of elements with one prescribed trace

Arpan Chandra Mazumder, Himangshu Hazarika, Dhiren Kumar Basnet +1

Let $q, n, m \in N$ such that $q$ is a prime power, $m \geq 3$ and $a \in F$ . We establish a sufficient condition for the existence of a primitive normal pair ($α…

math.NT2022

Characteristic functions for \MakeLowercase{(r, n)}-free and \MakeLowercase{(f, g)}-free elements

Himangshu Hazarika, Dhiren Kumar Basnet

For a prime power $q$ , $\F$ denotes the finite field of order $q$ , and for $m \geq 2$ , $\Fm$ denotes the extension field of degree $m$ . We establish a characteristic function for th…

math.RA2022

Pair of primitive elements in quadratic form with prescribed trace over a finite field

Himangshu Hazarika, Dhiren Kumar Basnet

In this article, we establish a sufficient condition for the existence of primitive element $α\in \Fm$ is such that $f (α)$ is also primitive element of $\Fm$ and $Tr_{\Fm/\F}(α)=β$…

math.NT2020

On existence of primitive normal elements of rational form over finite fields of even characteristic

Himangshu Hazarika, Dhiren Kumar Basnet, Giorgos Kapetanakis

Let $q$ be an even prime power and $m \geq 2$ an integer. By $F_{q}$ , we denote the finite field of order $q$ and by $F_{q^{m}}$ its extension degree $m$ . In this paper…

math.NT2020

The existence of primitive normal elements of quadratic forms over finite fields

Himangshu Hazarika, Dhiren Kumar Basnet, Stephen D Cohen

For $q = 3^{r}$ ( $r > 0$ ), denote by $F_{q}$ the finite field of order $q$ and for a positive integer $m \geq 2$ , let $F_{q^{m}}$ be its extension field of degree $m$ . We est…

math.AC2019★ 1 cited

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

Himangshu Hazarika, Dhiren Kumar Basnet

Let $F_{q^{n}}$ be the extension of the field $F_{q}$ 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 prov…