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Abstract Let { {K}} K be any field, let X P^k-1 X ⊂ P k - 1 be a set of n n distinct { {K}} K -rational points, and let a 1 a ≥ 1 be an integer. In this paper we find lower bounds for the minimum distance d (X) ₐ d (X) a of the evaluation code of order a a associated to X X. The first results use (X) α (X), the initial degree of the defining ideal of X X, and the bounds are true for any set X X. In another result we use s (X) s (X), the minimum socle degree, to find a lower bound for the case when X X is in general linear position. In both situations we improve and generalize known results.
Pawlina et al. (Fri,) studied this question.