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• W1963822025 abstract "We define the notion of weighted projective Reed–Muller codes over a subset X ⊂ P ( w 1 , … , w s ) of a weighted projective space over a finite field. We focus on the case when X is a projective weighted torus. We show that the vanishing ideal of X is a lattice ideal and relate it with the lattice ideal of a minimal presentation of the semigroup algebra of the numerical semigroup Q = 〈 w 1 , … , w s 〉 ⊂ N . We compute the index of regularity of the vanishing ideal of X in terms of the weights of the projective space and the Frobenius number of Q . We compute the basic parameters of weighted projective Reed–Muller codes over a 1-dimensional weighted torus and prove they are maximum distance separable codes." @default.
• W1963822025 created "2016-06-24" @default.
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• W1963822025 date "2015-05-01" @default.
• W1963822025 modified "2023-10-17" @default.
• W1963822025 title "Codes over a weighted torus" @default.
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• W1963822025 doi "https://doi.org/10.1016/j.ffa.2014.11.009" @default.
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