Low-degree Planar Monomials in Characteristic Two
نویسندگان
چکیده
Planar functions over finite fields give rise to finite projective planes and other combinatorial objects. They exist only in odd characteristic, but recently Zhou introduced an even characteristic analogue which has similar applications. In this paper we determine all planar functions on Fq of the form c 7→ act , where q is a power of 2, t is an integer with 0 < t ≤ q1/4, and a ∈ Fq. This settles and sharpens a conjecture of Schmidt and Zhou.
منابع مشابه
On the classification of planar monomials over fields of square order
Let Fq be a finite field of characteristic p and Fq [X] denote the ring of polynomials in X over Fq . A polynomial f ∈ Fq [X] is called a permutation polynomial over Fq if f induces a bijection of Fq under substitution. A polynomial f ∈ Fq [X] is said to be planar over Fq if for every non-zero a ∈ Fq , the polynomial f(X+a)−f(X) is a permutation polynomial over Fq . Planar polynomials have only...
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