Betti Numbers and Higher Weight Spectra of Reed-Muller Codes $R{M}_q(2,2)$

Sudhir R. Ghorpade, Trygve Johnsen, Rati Ludhani +1

We determine all the Betti numbers of the $q$-ary second order Reed-Muller codes of length $q^2$, and also of the elongations of matroids associated to these codes. We then use it…