Work

Hyper-derivative Algebraic Geometry Codes via Local Expansions

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.18098

Authors: Liu, Xiaofeng, Liu, Hengfeng, Zhang, Jun, Fu, Fang-Wei, Tang, Chunming

Institution: Nankai University

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Nankai University, Nankai Zhide Foundation, National Key Research and Development Program of China, Fundamental Research Funds for the Central Universities

Awards: G1176190679, G1704526169, G4015711035, G4579197882, G5563798569, G5903945647, G6328393359, G6455341836, G8759270399, G8890425352

OpenAlex ID: W7213523297

Cites:

Cited by:

Related to: