Yu et al. described an algorithm for conducting computational searches for quadratic APN functions over the finite field \(\mathbb {F}_{2^n}\) , and used this algorithm to give a classification of all quadratic APN functions with coefficients in \(\mathbb {F}_{2}\) for dimensions n up to 9. In this paper, we speed up the running time of that algorithm by a factor of approximately \(\frac{2^n}{n^2}\) . Based on this result, we give a complete classification of all quadratic APN functions over \(\mathbb {F}_{2^{10}}\) with coefficients in \(\mathbb {F}_{2}\) . We also perform some partial computations for quadratic APN functions with coefficients in \(\mathbb {F}_{2}\) over \(\mathbb {F}_{2^{11}}\) , and conjecture that they form 6 CCZ-inequivalent classes which also correspond to known APN functions.
