Isometry-Dual Flags of Many-Point AG Codes
Maria Bras-Amorós, Alonso S. Castellanos, Luciane Quoos · SIAM Journal on Applied Algebra and Geometry · 2023
Abstract. A flag of linear codes [Formula: see text] is said to have the isometry-dual property if there exists a vector [Formula: see text] such that [Formula: see text], where [Formula: see text] denotes the dual code of the code [Formula: see text]. We extend our previous results in [M. Bras-Amorós, A. S. Castellanos, and L. Quoos, IEEE Trans. Inform. Theory, 68 (2022), pp. 828–838] of flags of algebraic geometry two-point codes over a function field [Formula: see text] to flags of [Formula: see text]-point codes [Formula: see text][Formula: see text] for any tuple of integers [Formula: see text] and for an increasing sequence of integers [Formula: see text], just provided that [Formula: see text], where [Formula: see text] is the genus of [Formula: see text]. We apply the obtained results to the broad class of Kummer extensions defined by affine equations of the form [Formula: see text] for [Formula: see text], a separable polynomial of degree [Formula: see text], where [Formula: see text]. In particular, we obtain necessary and sufficient conditions on [Formula: see text] and [Formula: see text]’s such that the flag has the isometry-dual property.