Verifying the computed weight distribution for the binary Reed–Muller Code R(4,9)

We revisit pivotal aspects of computing the weight distribution of the binary Reed– Muller code R(4, 9) and introduce a verification technique based on the Heninger– Rains–Sloane integrality congruences for Reed–Muller codes. The consistency checks fully confirm the correctness of the distribution obtained in our previous work: “The weight distribution of the fourth-order Reed–Muller code of length 512”, Designs, Codes and Cryptography 93, 2487–2502 (2025).