We compute the weight distribution of the ${\mathcal R} (4,9)$ by combining the approach described in D. V. Sarwate's Ph.D. thesis from 1973 with knowledge on the affine equivalence classification of Boolean functions. To solve this problem posed, e.g., in the MacWilliams and Sloane book [p. 447], we apply a refined approach based on the classification of Boolean quartic forms in $8$ variables due to Ph. Langevin and G. Leander, and recent results on the classification of the quotient space ${\mathcal R} (4,7)/{\mathcal R} (2,7)$ due to V. Gillot and Ph. Langevin.

翻译：我们结合D. V. Sarwate 1973年博士论文中所述的方法与布尔函数的仿射等价分类知识，计算了${\mathcal R} (4,9)$的重量分布。为解决MacWilliams与Sloane著作[第447页]中提出的这一问题，我们采用了基于Ph. Langevin和G. Leander对8变量布尔四次型分类的精炼方法，并利用了V. Gillot与Ph. Langevin近期关于商空间${\mathcal R} (4,7)/{\mathcal R} (2,7)$的分类结果。