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

Computing the Weight Distribution of the Binary Reed-Muller Code ${\mathcal R} (4,9)$