Classification of quadratic APN functions with coefficients in F₂ in dimension 10

Yu et al. described an algorithm for conducting computational searches for quadratic APN functions over the finite field F2ⁿ , and used this algorithm to give a classification of all quadratic APN functions with coefficients in F₂ for dimensions n up to 9. In this paper, we speed up the running time of that algorithm by a factor of approximately 2ⁿ/n² . Based on this result, we give a complete classification of all quadratic APN functions over F_2¹⁰ with coefficients in F₂ . We also perform some partial computations for quadratic APN functions with coefficients in F₂ over F_2¹¹ , and conjecture that they form 6 CCZ-inequivalent classes which also correspond to known APN functions.