Trygve Johnsen

Betti Numbers and Higher Weight Spectra of Reed–Muller Codes \({\textrm{RM}}_{{q}}{(2,2)}\)

Abstract. We determine all the Betti numbers of the [Formula: see text]-ary second order Reed–Muller codes of length [Formula: see text], and also of the elongations of matroids associated to these codes. We then use it to determine the higher weight spectra of these codes. As a...