On the order bound of one-point algebraic geometry codes |
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Authors: | Anna Oneto |
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Institution: | a Ditpem, Università di Genova, P.le Kennedy, Pad. D -16129 Genova, Italy b Dima, Università di Genova, Via Dodecaneso 35 - 16146 Genova, Italy |
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Abstract: | Let S={si}i∈N⊆N be a numerical semigroup. For each i∈N, let ν(si) denote the number of pairs (si−sj,sj)∈S2: it is well-known that there exists an integer m such that the sequence {ν(si)}i∈N is non-decreasing for i>m. The problem of finding m is solved only in special cases. By way of a suitable parameter t, we improve the known bounds for m and in several cases we determine m explicitly. In particular we give the value of m when the Cohen-Macaulay type of the semigroup is three or when the multiplicity is less than or equal to six. When S is the Weierstrass semigroup of a family {Ci}i∈N of one-point algebraic geometry codes, these results give better estimates for the order bound on the minimum distance of the codes {Ci}. |
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Keywords: | 20M14 94B35 |
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