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Related Articles from SNS
Betti Numbers and Higher Weight Spectra of Reed-Muller Codes $RM_q(2,2)$
arXiv:2408.02548v3 Announce Type: replace-cross Abstract: 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 to determine the higher weight spectra of these codes. As a special case, we recover some results of Kaplan and Matei about counting certain curves over finite fields with prescribed rational intersection points.