Hyper-derivative Algebraic Geometry Codes via Local Expansions

2026-09-16

AI Summary

本文通过局部展开构建了超导数代数几何码，扩展了超导数Reed-Solomon码至一般代数函数域，并利用留数定理确定其对偶性质及自正交和自对偶的条件。

Abstract

In this paper, we develop a systematic construction framework of hyper-derivative algebraic geometry codes via local expansions, extending hyper-derivative Reed-Solomon codes from the rational function field to general algebraic function fields. Using the residue theorem, we determine their Euclidean duals and illustrate that the duals naturally reverse. We further give criteria for reverse self orthogonality and reverse self duality in terms of two classes of bilinear forms. Finally, we provide an asymptotic bound on the rate and relative distance via function field towers.

Problem

• hyper-derivative algebraic geometry codes
• local expansions
• Euclidean duals
• reverse self orthogonality
• asymptotic bound

Innovation

• hyper-derivative algebraic geometry codes
• local expansions
• residue theorem
• reverse self orthogonality
• function field towers