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：我们通过结合D. V. Sarwate于1973年博士论文中提出的方法，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。为了解决这一被MacWilliams与Sloane著作[第447页]所提及的开放问题，我们采用了基于Ph. Langevin和G. Leander关于8变量布尔四次型分类的精化方法，并结合V. Gillot与Ph. Langevin近期关于商空间${\mathcal R} (4,7)/{\mathcal R} (2,7)$分类的研究成果。