Generalized Hamming weights of toric codes over hypersimplices and squarefree affine evaluation codes

Let $ \mathbb{F}_{q} be a finite field with q elements, where is power of prime p $. A polynomial over monomially squarefree if all its monomials are squarefree. In this paper, we determine an upper bound on the number common zeroes any set r linearly independent polynomials \mathbb{F}_{q}[t_{1}, t_{2}, \dots, t_{s}] in affine torus T = (\mathbb{F}_{q}^{*})^{s} under certain conditions $, s and degree these polynomials. Applying results, obtain generalized Hamming weights toric codes hypersimplices evaluation codes, as defined [14].