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• W2068180810 abstract "Classical planar functions are functions from a finite field to itself and give rise to finite projective planes. They exist however only for fields of odd characteristic. We study their natural counterparts in characteristic two, which we also call planar functions. They again give rise to finite projective planes, as recently shown by the second author. We give a characterisation of planar functions in characteristic two in terms of codes over $mathbb {Z}_{4}$ . We then specialise to planar monomial functions f(x)=cx t and present constructions and partial results towards their classification. In particular, we show that t=1 is the only odd exponent for which f(x)=cx t is planar (for some nonzero c) over infinitely many fields. The proof techniques involve methods from algebraic geometry." @default.
• W2068180810 created "2016-06-24" @default.
• W2068180810 creator A5039613345 @default.
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• W2068180810 date "2014-01-09" @default.
• W2068180810 modified "2023-09-27" @default.
• W2068180810 title "Planar functions over fields of characteristic two" @default.
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• W2068180810 doi "https://doi.org/10.1007/s10801-013-0496-z" @default.
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