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Hyper-derivative Algebraic Geometry Codes via Local Expansions

  • Xiaofeng Liu
  • Hengfeng Liu
  • Jun Zhang
  • Fang-Wei Fu
  • Chunming Tang
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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.

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Cite

BibTeXRIS
BibTeX
@misc{liu2026hyperderivative,
  title = {{Hyper-derivative Algebraic Geometry Codes via Local Expansions}},
  author = {Xiaofeng Liu and Hengfeng Liu and Jun Zhang and Fang-Wei Fu and Chunming Tang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18098},
  eprint = {2609.18098},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18098},
}
RIS
TY  - UNPB
TI  - Hyper-derivative Algebraic Geometry Codes via Local Expansions
AU  - Xiaofeng Liu
AU  - Hengfeng Liu
AU  - Jun Zhang
AU  - Fang-Wei Fu
AU  - Chunming Tang
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18098
UR  - https://arxiv.org/abs/2609.18098
AB  - 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.
ER  -