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

Consider a sequence of AG codes evaluating at a set of evaluation points P1, . . . , Pn 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.