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Let p be an odd prime, k, be positive integers, q=pᵏ, Q=p^. In this paper we characterise planar functions of the form f₂ (X) =c₀X^qQ+q+c₁X^qQ+1+c₂X^Q+q+c₃X^Q+1 over Fₐℂ for any c= (c₀, c₁, c₂, c₃) Fₐℂ⁴ in terms of linear equivalence.
Chan et al. (Mon,) studied this question.