Higher Weight Spectra of Veronese Codes.

We study ${q}$ -ary linear codes ${C}$ obtained from Veronese surfaces over finite fields. We show how one can find the higher weight spectra of these codes, or equivalently, the weight distribution of all extension codes of ${C}$ over all field extensions of $\mathbb {F}_{q}$. Our methods will be a study of the Stanley-Reisner rings of a series of matroids associated to each code ${C}$. [ABSTRACT FROM AUTHOR]