Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: nucl-th