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arXiv · 1702.08225

On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups

J. I. Farrán·P. A. García-Sánchez·B. A. Heredia
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Abstract

We describe the second (generalized) Feng-Rao distance for elements in an Arf numerical semigroup that are greater than or equal to the conductor of the semigroup. This provides a lower bound for the second Hamming weight for one point AG codes. In particular, we can obtain the second Feng-Rao distance for the codes defined by asymptotically good towers of function fields whose Weierstrass semigroups are inductive. In addition, we compute the second Feng-Rao number, and provide some examples and comparisons with previous results on this topic. These calculations rely on Ap\'{e}ry sets, and thus several results concerning Ap\'ery sets of Arf semigroups are presented.

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J. I. Farrán, P. A. García-Sánchez, B. A. Heredia. 2017-02-27. On the second Feng-Rao distance of Algebraic Geometry codes related to Arf semigroups. https://arxiv.org/abs/1702.08225

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