Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Planar functions and perfect nonlinear monomials over finite fields   The study of finite projective planes involves planar functions, namely,
functions f : F_q --> F_q such that, for each nonzero a in F_q, the function c
--> f(c+a) - f(c) is a bijection on F_q. Planar functions are also used in the
construction of DES-like cryptosystems, where they are called perfect nonlinear
functions. We determine all planar functions on F_q of the form c --> c^t,
under the assumption that q >= (t-1)^4. This implies two conjectures of
Hernando, McGuire and Monserrat. Our arguments also yield a new proof of a
conjecture of Segre and Bartocci from 1971 about monomial hyperovals in finite
Desarguesian projective planes.

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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: dg-ga