Improved Subexponential Upper Bounds for $3$-Restricted Matching Vector Families

[2608.27859] Improved Subexponential Upper Bounds for $3$-Restricted Matching Vector Families Skip to main content Search Submit Donate Log in Computer Science > Computational Complexity arXiv:2608.27859 (cs) [Submitted on 28 Aug 2026] Title: Improved Subexponential Upper Bounds for $3$-Restricted Matching Vector Families Authors: Sidhant Saraogi View PDF HTML (experimental) Abstract: Matching Vector families (MVFs) are defined by two ordered lists of vectors in $\mathbb{Z}_m^n$ whose inner products satisfy specific residue patterns modulo an integer $m$. Most famously, restricted MVFs are used to construct the best-known constant-query Locally Decodable codes (LDCs). We prove an upper bound of $2^{O\left(\sqrt{n\log n \log m}\right)}$ on the size of $3$-restricted MVFs in $\mathbb{Z}_m^n$ for $m \leq \sqrt{n}$, substantially improving on the previous best bound of $2^{O(n/\log n)}$ by Bhowmick, Dvir and Lovett (STOC'13, SICOMP'14). Our proof relies on a new polynomial method argument that controls collisions in sumsets of matching vectors. Comments: 11 pages Subjects: Computational Complexity (cs.CC) ; Discrete Mathematics (cs.DM); Information Theory (cs.IT) Cite as: arXiv:2608.27859 [cs.CC] (or arXiv:2608.27859v1 [cs.CC] for this version) https://doi.org/10.48550/arXiv.2608.27859 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sidhant Saraogi [ view email ] [v1] Fri, 28 Aug 2026 03:08:39 UTC (24 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.CC < prev | next > new | recent | 2026-08 Change to browse by: cs cs.DM cs.IT math math.IT References & Citations SciX 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)

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