B. Sharma

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math.NT2026

On Consecutive Non-primitive Elements over Finite Fields

Bidushi Sharma, Dhiren Kumar Basnet

In this article, we establish a bound on $θ_{q}$ that guarantees the existence of a pair of consecutive non-primitive elements in $F_{q}$ , with the exceptions $q = 4$ and $q = 8$ .…

math.NT2026

On some Non-Permutations of Quadratic Extension of Finite Field

Bidushi Sharma, Dhiren Kumar Basnet

In this article, we study polynomials over $F_{q^{2}}$ that do not permute $F_{q^{2}}$ . More precisely, we characterize polynomials of the forms $x^q + b x^2 + c x +…

math.NT2024

Construction of Permutation Polynomials over Finite Fields with the help of SCR polynomials

Bidushi Sharma, Dhiren Kumar Basnet

In this paper we take a deeper look at the self conjugate reciprocal (SCR) polynomials, which towards the end of the paper aid the construction of new classes of permutation polyno…