Higher weight spectra and Betti numbers of Reed-Muller codes

SR Ghorpade, T Johnsen, R Ludhani… - arXiv preprint arXiv …, 2024 - arxiv.org
We determine the higher weight spectra of $ q $-ary Reed-Muller codes $ C_q= RM_q (2, 2)
$ for all prime powers $ q $. This is equivalent to finding the usual weight distributions of all …