The 0-APN Power Functions over 𝔽2n and Their Applications to Linear Codes

The partially APN function attracted researchers’ particular interest recently. It plays an important role in studying APN functions and linear codes with the minimum distance [Formula: see text]. In this paper, based on the multivariate method and resultant elimination, we propose several new infinite classes of [Formula: see text]-APN power functions over [Formula: see text]. Furthermore, two infinite classes of [Formula: see text]-APN power functions [Formula: see text] over [Formula: see text] are characterized completely where [Formula: see text] or [Formula: see text] for some positive integers [Formula: see text]. Finally, we give an application of [Formula: see text]-APN power functions in binary linear codes.