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 年博士论文中描述的方法以及关于布尔函数仿射等价分类的知识，计算了 ${\mathcal R} (4,9)$ 的重量分布。为解决这一在 MacWilliams 与 Sloane 的著作 [第 447 页] 中提出的问题，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，以及 V. Gillot 和 Ph. Langevin 关于商空间 ${\mathcal R} (4,7)/{\mathcal R} (2,7)$ 分类的最新成果。