Generalized Hamming weight of Projective Toric Code over Hypersimplices
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The d-th hypersimplex of R^s is the convex hull in R^s of all integral points e_i_1+e_i_2+...+e_i_d such that 1 ≤ i_1 <... < i_d≤ s where e_i is the i-th unit vector in R^s. In [1], the authors have defined projective toric code of P of degree d denoted by C_P(d) and computed its dimension and minimum distance. In this note, we compute the second generalized Hamming weight of these codes. We also calculated the r-th generalized Hamming weight (1 ≤ r ≤ dim(C_P(d))) in certain cases.
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