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arXiv · 1707.04062

A Note on the Inheritance of the Isometry-Dual Property under Puncturing AG Codes

Maria Bras-Amorós
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Abstract

Consider a sequence of AG codes evaluating at a set of evaluation points $P_1,\dots,P_n$ the functions having only poles at a defining point $Q$, with the sequence of codes satisfying the isometry-dual condition (i.e. containing at the same time primal and their dual codes). We prove a necessary condition under which, after taking out a number of evaluation points (i.e. puncturing), the resulting AG codes can still satisfy the isometry-dual property. The condition has to do with the so-called maximum sparse ideals of the Weierstrass semigroup of $Q$.

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Maria Bras-Amorós. 2017-07-13. A Note on the Inheritance of the Isometry-Dual Property under Puncturing AG Codes. https://arxiv.org/abs/1707.04062

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