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arXiv · 2104.01942

Counterexamples to Dembowski and Ostrom conjecture on Planar function

Rajesh P. Singh
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Abstract

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.

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Rajesh P. Singh. 2021-04-05. Counterexamples to Dembowski and Ostrom conjecture on Planar function. https://arxiv.org/abs/2104.01942

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