Classification of a class of planar polynomials

Let p be an odd prime, k, be positive integers, q=pᵏ, Q=p^. In this paper we characterise planar functions of the form f_c(X)=c₀XqQ+q+c₁XqQ+1+c₂XQ+q+c₃XQ+1 over Fq² for any c=(c₀,c₁,c₂,c₃) ∈ Fq²⁴ in terms of linear equivalence.