arXiv subjects

Rajesh P. Singh

Publications and source records attributed to Rajesh P. Singh.

2 recordsLinked to original sources

arXiv2026

Inverses of six classes of permutation polynomials of the form $x+γ\operatorname{Tr}_q^{q^2}(h(x))$ over finite fields of even characteristic

Recently, Jiang et al. \cite{JIANG2025102522} obtained several classes of Permutation Polynomial of the form $x+γ\operatorname{Tr}_q^{q^2}(h(x))$ over finite fields $\mathbb{F}_{q^2},q=2^n$. In this paper, we find the compositional inverse of six classes of permutation polynomials of this form.

math.NT↗

arXiv2021

Counterexamples to Dembowski and Ostrom conjecture on Planar function

Let $F_{q}$ be a finite field of cardinality $q$. A polynomial over finite field $F_{q}$ of the form $\sum_{i,j}a_{ij}x^{p^{i}+p^{j}}$ is called a Dembowski-Ostrom (DO) polynomial. The Dembowski-Ostrom conjecture says that a planar polynomial is necessarily a Dembowski-Ostrom polynomial. In this article, we construct certain classes of planar polynomials over any finite field of characteristic $p\geq 3$ that are not of Dembowski-Ostrom type.

math.NT↗