Lifting iso-dual algebraic geometry codes

[2311.08992] Lifting iso-dual algebraic geometry codes Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Information Theory arXiv:2311.08992 (cs) [Submitted on 15 Nov 2023 ( v1 ), last revised 15 Apr 2026 (this version, v2)] Title: Lifting iso-dual algebraic geometry codes Authors: María Chara , Ricardo Podestá , Luciane Quoos , Ricardo Toledano View a PDF of the paper titled Lifting iso-dual algebraic geometry codes, by Mar\'ia Chara and 3 other authors View PDF HTML (experimental) Abstract: In this work we investigate the problem of producing iso-dual algebraic geometry (AG) codes over a finite field $\mathbb{F}_q$ with $q$ elements. Given a finite separable extension $\mathcal{M}/\mathcal{F}$ of function fields and an iso-dual AG-code $\mathcal{C}$ defined over $\mathcal{F}$, we provide a general method to lift the code $\mathcal{C}$ to another iso-dual AG-code $\tilde{\mathcal{C}}$ defined over $\mathcal{M}$ under some assumptions on the divisors $D$ and $G$ and on the parity of the involved different exponents. We apply this method to lift iso-dual AG-codes over the rational function field to elementary abelian $p$-extensions, like the maximal function fields defined by the Hermitian, Suzuki, and one covered by the $GGS$ function field. We also obtain long binary and ternary iso-dual AG-codes defined over cyclotomic extensions. Comments: This manuscript is a corrected version of the paper "Good iso-dual AG-codes from towers of function fields'', published in Designs, Codes and Cryptography, Volume 92, pages 2743-2767 (2024), where the corrections do not affect the main results Subjects: Information Theory (cs.IT) ; Number Theory (math.NT) MSC classes: 11T71, 14G50, 94B05, 94B27 (primary) Cite as: arXiv:2311.08992 [cs.IT] (or arXiv:2311.08992v2 [cs.IT] for this version) https://doi.org/10.48550/arXiv.2311.08992 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ricardo Alberto Podestá [ view email ] [v1] Wed, 15 Nov 2023 14:25:35 UTC (32 KB) [v2] Wed, 15 Apr 2026 02:00:16 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled Lifting iso-dual algebraic geometry codes, by Mar\'ia Chara and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.IT < prev | next > new | recent | 2023-11 Change to browse by: cs math math.IT math.NT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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