On homogeneous planar functions

2013/12/11 by Tao Feng, Feng, Tao
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1312.3620

openalex publication_date 2013/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be an odd prime and \F_q be the finite field with q=pⁿ elements. A planar function f:\F_q→\F_q is called homogenous if f(λx)=λ^df(x) for all λ∈\F_p and x∈\F_q, where d is some fixed positive integer. We characterize x² as the unique homogenous planar function over \F_p² up to equivalence.

Citations

• Planar functions over fields of characteristic two

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