Non-RS MDS Codes via Row-Column Twists

[2509.06919] Non-RS MDS Codes via Row-Column Twists Skip to main content Search Submit Donate Log in Computer Science > Information Theory arXiv:2509.06919 (cs) [Submitted on 8 Sep 2025 ( v1 ), last revised 24 Aug 2026 (this version, v2)] Title: Non-RS MDS Codes via Row-Column Twists Authors: Anuj Kumar Bhagat , Harshdeep Singh , Ritumoni Sarma View PDF HTML (experimental) Abstract: This article introduces a new class of codes, called row-column twisted Reed--Solomon (RCTRS) codes, motivated by the constructions in (Beelen et al. \cite{beelen2017twisted}) and (Liu et al. \cite{liu2025column}). Explicit conditions under which RCTRS codes are MDS are established, and their existence is proved by algebraic techniques. By deriving lower bounds on the dimensions of their Schur squares, it is shown that these MDS codes, as well as their extended codes, are not equivalent to Reed--Solomon codes, and hence form new families of non-RS MDS codes. It is further proved that they are not equivalent to column twisted Reed--Solomon codes or their extended versions, and, when the hook lies strictly between the two extreme positions, are not equivalent to twisted Reed--Solomon codes with twist $t = 1$ either. Introducing twists in both a row and a column therefore yields a family of MDS codes distinct from the previously known constructions. Subjects: Information Theory (cs.IT) Cite as: arXiv:2509.06919 [cs.IT] (or arXiv:2509.06919v2 [cs.IT] for this version) https://doi.org/10.48550/arXiv.2509.06919 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Anuj Kumar Bhagat [ view email ] [v1] Mon, 8 Sep 2025 17:30:03 UTC (19 KB) [v2] Mon, 24 Aug 2026 18:20:00 UTC (28 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: cs.IT < prev | next > new | recent | 2025-09 Change to browse by: cs math math.IT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation 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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