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Weight Distribution of the Binary Reed-Muller Code R(4,9)
  • Miroslav Markov,
  • Yuri Borissov
Miroslav Markov
Yuri Borissov

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We compute the weight distribution of 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 [12, p. 447], we apply a refined approach based on the classification of Boolean quartic forms in eight variables due to Ph. Langevin and G. Leander, and recent results on the classification of the quotient space R(4, 7)/R(2, 7) due to V. Gillot and Ph. Langevin.
17 Dec 2023Submitted to TechRxiv
22 Dec 2023Published in TechRxiv