Verifying the computed weight distribution for the binary Reed–Muller Code R(4,9)
DOI:
https://doi.org/10.55630/mem.2026.55.340-349Keywords:
binary Reed–Muller code, weight distribution, affine equivalenceAbstract
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).
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