The Isometry-Dual Property in Flags of Two-Point Algebraic Geometry Codes

The dual geometry of Hermitian two-point codes

In this paper we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases.

On the order bound of one-point algebraic geometry codes

1 Abstract. Let S ={si}i∈IN ⊆ IN be a numerical semigroup. For each i ∈ IN, let ν(si) denote the number of pairs (si−sj , sj) ∈ S: it is well-known that there exists an integer m such that the sequence {ν(si)}i∈IN 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 dete...

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 ...

Algebraic Geometry Codes

Algebraic-Geometry Codes