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A Simple Sub-Polynomial Degree Coboundary Expander

Authors Max Hopkins , Arka Ray

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
  • Theory of computation → Pseudorandomness and derandomization
Keywords
  • high dimensional expansders
  • agreement testing
  • probabilistically checkable proofs

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Abstract

High dimensional expanders simultaneously satisfying spectral and combinatorial (coboundary) expansion have recently played a major role in breakthroughs in PCP and coding theory, but the only known construction of such complexes is extremely involved, requiring deep algebraic number theory. In this work, we give an extremely simple combinatorial construction of a sub-polynomial degree complex based on projections of the flags complex (subspace chains) that is (i) a local spectral expander, (ii) a coboundary expander, and (iii) a swap coboundary expander. As a corollary, we also give the first near-linear size combinatorial hypergraphs with good agreement tests in the `1%' regime, and a simple PCP construction with near-linear size.

Cite As Get BibTex

Max Hopkins and Arka Ray. A Simple Sub-Polynomial Degree Coboundary Expander. In 41st Computational Complexity Conference (CCC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 383, pp. 26:1-26:41, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CCC.2026.26

Author Details

Max Hopkins
  • Institute for Advanced Study, Princeton, NJ, USA
Arka Ray
  • Indian Institute of Science, Bengaluru, India

Funding

  • Hopkins, Max: Supported by NSF Award DMS-2424441.
  • Ray, Arka: Supported in part by the Walmart Center for Tech Excellence at IISc (CSR Grant WMGT-23-0001).

Acknowledgements

We thank Yotam Dikstein and Roy Meshulam for helpful discussions. We are grateful to the International Centre for Theoretical Sciences (ICTS) for organizing the "ICTS Workshop on HDXs and Codes" (code: ICTS/HDXandCodes2025/04) which greatly facilitated our discussions with Roy Meshulam. We thank the anonymous reviewers of CCC 2026 for their comments and suggestions.

References

  1. Dorna Abdolazimi and Shayan Oveis Gharan. An improved trickle down theorem for partite complexes. In Proceedings of the conference on Proceedings of the 38th Computational Complexity Conference, pages 1-16, 2023. URL: https://doi.org/10.4230/LIPIcs.CCC.2023.10.
  2. Vedat Levi Alev, Fernando Granha Jeronimo, Dylan Quintana, Shashank Srivastava, and Madhur Tulsiani. List decoding of direct sum codes. In Shuchi Chawla, editor, Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, UT, USA, January 5-8, 2020, pages 1412-1425. SIAM, 2020. URL: https://doi.org/10.1137/1.9781611975994.85.
  3. Vedat Levi Alev, Fernando Granha Jeronimo, and Madhur Tulsiani. Approximating constraint satisfaction problems on high-dimensional expanders. In 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, pages 180-201. IEEE Comput. Soc. Press, Los Alamitos, CA, [2019] ©2019. URL: https://doi.org/10.1109/FOCS.2019.00021.
  4. Noga Alon. Eigenvalues and expanders. Combinatorica, 6(2):83-96, 1986. URL: https://doi.org/10.1007/BF02579166.
  5. Noga Alon and Vitali D Milman. λ₁, isoperimetric inequalities for graphs, and superconcentrators. Journal of Combinatorial Theory, Series B, 38(1):73-88, 1985. Google Scholar
  6. Nima Anari, Vishesh Jain, Frederic Koehler, Huy Tuan Pham, and Thuy-Duong Vuong. Entropic independence: optimal mixing of down-up random walks. In Stefano Leonardi and Anupam Gupta, editors, STOC '22: 54th Annual ACM SIGACT Symposium on Theory of Computing, Rome, Italy, June 20 - 24, 2022, pages 1418-1430. ACM, 2022. URL: https://doi.org/10.1145/3519935.3520048.
  7. Nima Anari, Kuikui Liu, and Shayan Oveis Gharan. Spectral independence in high-dimensional expanders and applications to the hardcore model. SIAM J. Comput., 53(6):S20-1, 2024. URL: https://doi.org/10.1137/20M1367696.
  8. Nima Anari, Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant. Log-concave polynomials II: High-dimensional walks and an FPRAS for counting bases of a matroid. In STOC'19 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pages 1-12. ACM, New York, 2019. URL: https://doi.org/10.1145/3313276.3316385.
  9. Nima Anari, Kuikui Liu, Shayan Oveis Gharan, Cynthia Vinzant, and Thuy-Duong Vuong. Log-concave polynomials IV: approximate exchange, tight mixing times, and near-optimal sampling of forests. In Samir Khuller and Virginia Vassilevska Williams, editors, STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21-25, 2021, pages 408-420. ACM, 2021. URL: https://doi.org/10.1145/3406325.3451091.
  10. Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy. Proof verification and the hardness of approximation problems. J. ACM, 45(3):501-555, 1998. URL: https://doi.org/10.1145/278298.278306.
  11. Sanjeev Arora and Shmuel Safra. Probabilistic checking of proofs: A new characterization of NP. J. ACM, 45(1):70-122, 1998. URL: https://doi.org/10.1145/273865.273901.
  12. Mitali Bafna, Noam Lifshitz, and Dor Minzer. Constant degree direct product testers with small soundness. In 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS), pages 862-869. IEEE, 2024. URL: https://doi.org/10.1109/FOCS61266.2024.00059.
  13. Mitali Bafna and Dor Minzer. Characterizing direct product testing via coboundary expansion. In Bojan Mohar, Igor Shinkar, and Ryan O'Donnell, editors, Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, Vancouver, BC, Canada, June 24-28, 2024, pages 1978-1989. ACM, 2024. URL: https://doi.org/10.1145/3618260.3649714.
  14. Mitali Bafna, Dor Minzer, Nikhil Vyas, and Zhiwei Yun. Quasi-linear size pcps with small soundness from HDX. CoRR, abs/2407.12762, 2024. URL: https://doi.org/10.48550/arXiv.2407.12762.
  15. Mitali Bafna, Dor Minzer, Nikhil Vyas, and Zhiwei Yun. Quasi-linear size PCPs with small soundness from HDX. In Michal Koucký and Nikhil Bansal, editors, Proceedings of the 57th Annual ACM Symposium on Theory of Computing, STOC 2025, Prague, Czechia, June 23-27, 2025, pages 45-53. ACM, 2025. URL: https://doi.org/10.1145/3717823.3718197.
  16. Anders Björner. Shellable and cohen-macaulay partially ordered sets. Transactions of the american mathematical society, 260(1):159-183, 1980. Google Scholar
  17. Michael Chapman and Alexander Lubotzky. Stability of homomorphisms, coverings and cocycles ii: Examples, applications and open problems. Advances in Mathematics, 463:110117, 2025. Google Scholar
  18. Mark De Longueville. A course in topological combinatorics. Springer Science & Business Media, 2013. Google Scholar
  19. Laura Grave de Peralta and Inga Valentiner-Branth. High-dimensional expanders from kac-moody-steinberg groups. European Journal of Combinatorics, 126:104131, 2025. URL: https://doi.org/10.1016/J.EJC.2025.104131.
  20. Philippe Delsarte. Association schemes and t-designs in regular semilattices. Journal of Combinatorial Theory, Series A, 20(2):230-243, 1976. URL: https://doi.org/10.1016/0097-3165(76)90017-0.
  21. Yotam Dikstein and Irit Dinur. Agreement testing theorems on layered set systems. In 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, pages 1495-1524. IEEE Comput. Soc. Press, Los Alamitos, CA, [2019] ©2019. URL: https://doi.org/10.1109/FOCS.2019.00088.
  22. Yotam Dikstein and Irit Dinur. Agreement theorems for high dimensional expanders in the low acceptance regime: The role of covers. In Bojan Mohar, Igor Shinkar, and Ryan O'Donnell, editors, Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, Vancouver, BC, Canada, June 24-28, 2024, pages 1967-1977. ACM, 2024. URL: https://doi.org/10.1145/3618260.3649685.
  23. Yotam Dikstein and Irit Dinur. Coboundary and cosystolic expansion without dependence on dimension or degree. In Amit Kumar and Noga Ron-Zewi, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2024, August 28-30, 2024, London School of Economics, London, UK, volume 317 of LIPIcs, pages 62:1-62:24. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.62.
  24. Yotam Dikstein and Irit Dinur. Swap cosystolic expansion. In Bojan Mohar, Igor Shinkar, and Ryan O'Donnell, editors, Proceedings of the 56th Annual ACM Symposium on Theory of Computing, STOC 2024, Vancouver, BC, Canada, June 24-28, 2024, pages 1956-1966. ACM, 2024. URL: https://doi.org/10.1145/3618260.3649780.
  25. Yotam Dikstein, Irit Dinur, Prahladh Harsha, and Noga Ron-Zewi. Locally testable codes via high-dimensional expanders. Electron. Colloquium Comput. Complex., TR20-072, 2020. URL: https://eccc.weizmann.ac.il/report/2020/072.
  26. Yotam Dikstein, Irit Dinur, and Alexander Lubotzky. Low acceptance agreement tests via bounded-degree symplectic hdxs. In 65th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2024, Chicago, IL, USA, October 27-30, 2024, pages 826-861. IEEE, 2024. URL: https://doi.org/10.1109/FOCS61266.2024.00058.
  27. Yotam Dikstein and Max Hopkins. Chernoff bounds and reverse hypercontractivity on hdx. In 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS), pages 870-919. IEEE, 2024. URL: https://doi.org/10.1109/FOCS61266.2024.00060.
  28. Yotam Dikstein, Max Hopkins, Russell Impagliazzo, and Toniann Pitassi. High rate efficient local list decoding from hdx. arXiv preprint arXiv:2601.22535, 2026. URL: https://doi.org/10.48550/arXiv.2601.22535.
  29. Yotam Dikstein, Siqi Liu, and Avi Wigderson. Sparser abelian high dimensional expanders. In Srikanth Srinivasan, editor, 40th Computational Complexity Conference, CCC 2025, Toronto, Canada, August 5-8, 2025, volume 339 of LIPIcs, pages 7:1-7:98. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. URL: https://doi.org/10.4230/LIPIcs.CCC.2025.7.
  30. Irit Dinur. The PCP theorem by gap amplification. J. ACM, 54(3):12, 2007. URL: https://doi.org/10.1145/1236457.1236459.
  31. Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, and Shahar Mozes. Locally testable codes with constant rate, distance, and locality. In Stefano Leonardi and Anupam Gupta, editors, STOC '22: 54th Annual ACM SIGACT Symposium on Theory of Computing, Rome, Italy, June 20 - 24, 2022, pages 357-374. ACM, 2022. URL: https://doi.org/10.1145/3519935.3520024.
  32. Irit Dinur, Yuval Filmus, Prahladh Harsha, and Madhur Tulsiani. Explicit sos lower bounds from high-dimensional expanders. In James R. Lee, editor, 12th Innovations in Theoretical Computer Science Conference, ITCS 2021, Virtual Conference, January 6-8, 2021, volume 185 of LIPIcs, pages 38:1-38:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ITCS.2021.38.
  33. Irit Dinur and Elazar Goldenberg. Locally testing direct product in the low error range. In 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008, Philadelphia, PA, USA, October 25-28, 2008, pages 613-622. IEEE Computer Society, 2008. URL: https://doi.org/10.1109/FOCS.2008.26.
  34. Irit Dinur and Prahladh Harsha. Composition of low-error 2-query pcps using decodable pcps. SIAM Journal on Computing, 42(6):2452-2486, 2013. URL: https://doi.org/10.1137/100788161.
  35. Irit Dinur and Tali Kaufman. High dimensional expanders imply agreement expanders. In 58th Annual IEEE Symposium on Foundations of Computer Science - FOCS 2017, pages 974-985. IEEE Computer Soc., Los Alamitos, CA, 2017. URL: https://doi.org/10.1109/FOCS.2017.94.
  36. Irit Dinur and Inbal Livni Navon. Exponentially small soundness for the direct product z-test. Theory Comput., 19:1-56, 2023. URL: https://doi.org/10.4086/TOC.2023.V019A003.
  37. Irit Dinur and Omer Reingold. Assignment testers: Towards a combinatorial proof of the PCP theorem. SIAM J. Comput., 36(4):975-1024, 2006. URL: https://doi.org/10.1137/S0097539705446962.
  38. Irit Dinur and David Steurer. Direct product testing. In IEEE 29th Conference on Computational Complexity, CCC 2014, Vancouver, BC, Canada, June 11-13, 2014, pages 188-196. IEEE Computer Society, 2014. URL: https://doi.org/10.1109/CCC.2014.27.
  39. Shai Evra and Tali Kaufman. Bounded degree cosystolic expanders of every dimension. In Proceedings of the forty-eighth annual ACM symposium on Theory of Computing, pages 36-48, 2016. URL: https://doi.org/10.1145/2897518.2897543.
  40. Shai Evra, Tali Kaufman, and Gilles Zémor. Decodable quantum LDPC codes beyond the square root distance barrier using high dimensional expanders. In Sandy Irani, editor, 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020, Durham, NC, USA, November 16-19, 2020, pages 218-227. IEEE, 2020. URL: https://doi.org/10.1109/FOCS46700.2020.00029.
  41. Uriel Feige, Shafi Goldwasser, László Lovász, Shmuel Safra, and Mario Szegedy. Interactive proofs and the hardness of approximating cliques. J. ACM, 43(2):268-292, 1996. URL: https://doi.org/10.1145/226643.226652.
  42. Uriya A. First and Tali Kaufman. On good 2-query locally testable codes from sheaves on high dimensional expanders. CoRR, abs/2208.01778, 2022. URL: https://doi.org/10.48550/arXiv.2208.01778.
  43. Jason Gaitonde, Max Hopkins, Tali Kaufman, Shachar Lovett, and Ruizhe Zhang. Eigenstripping, spectral decay, and edge-expansion on posets. In Amit Chakrabarti and Chaitanya Swamy, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022, September 19-21, 2022, University of Illinois, Urbana-Champaign, USA (Virtual Conference), volume 245 of LIPIcs, pages 16:1-16:24. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.16.
  44. Oded Goldreich and Shmuel Safra. A combinatorial consistency lemma with application to proving the PCP theorem. SIAM J. Comput., 29(4):1132-1154, 2000. URL: https://doi.org/10.1137/S0097539797315744.
  45. Louis Golowich. Improved product-based high-dimensional expanders. In Mary Wootters and Laura Sanità, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021, University of Washington, Seattle, Washington, USA (Virtual Conference), August 16-18, 2021, volume 207 of LIPIcs, pages 38:1-38:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2021.38.
  46. Louis Golowich. From grassmannian to simplicial high-dimensional expanders. In 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), pages 1639-1648. IEEE, 2023. URL: https://doi.org/10.1109/FOCS57990.2023.00099.
  47. Roy Gotlib and Tali Kaufman. List agreement expansion from coboundary expansion. In Yael Tauman Kalai, editor, 14th Innovations in Theoretical Computer Science Conference, ITCS 2023, January 10-13, 2023, MIT, Cambridge, Massachusetts, USA, volume 251 of LIPIcs, pages 61:1-61:23. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPIcs.ITCS.2023.61.
  48. M. Gromov. Singularities, expanders and topology of maps. part 2: from combinatorics to topology via algebraic isoperimetry. Geom. Funct. Anal., 20:416-526, 2010. URL: https://doi.org/10.1007/s00039-010-0073-8.
  49. Anna Gundert and Uli Wagner. On eigenvalues of random complexes. Israel Journal of Mathematics, 216:545-582, 2016. Google Scholar
  50. Tom Gur, Noam Lifshitz, and Siqi Liu. Hypercontractivity on high dimensional expanders. In Stefano Leonardi and Anupam Gupta, editors, STOC '22: 54th Annual ACM SIGACT Symposium on Theory of Computing, Rome, Italy, June 20 - 24, 2022, pages 176-184. ACM, 2022. URL: https://doi.org/10.1145/3519935.3520004.
  51. Tom Gur, Dor Minzer, Guy Weissenberg, and Kai Zhe Zheng. 3-query rldcs are strictly stronger than 3-query ldcs. arXiv preprint arXiv:2512.12960, 2025. URL: https://doi.org/10.48550/arXiv.2512.12960.
  52. Allen Hatcher. Algebraic topology. Cambridge University Press, 2002. Google Scholar
  53. Max Hopkins and Ting-Chun Lin. Explicit lower bounds against Ω(n)-rounds of sum-of-squares. In 63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022, Denver, CO, USA, October 31 - November 3, 2022, pages 662-673. IEEE, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00069.
  54. Jun-Ting Hsieh, Alexander Lubotzky, Sidhanth Mohanty, Assaf Reiner, and Rachel Yun Zhang. Explicit lossless vertex expanders. arXiv preprint arXiv:2504.15087, 2025. URL: https://doi.org/10.48550/arXiv.2504.15087.
  55. Russell Impagliazzo, Ragesh Jaiswal, Valentine Kabanets, and Avi Wigderson. Uniform direct product theorems: Simplified, optimized, and derandomized. SIAM J. Comput., 39(4):1637-1665, 2010. URL: https://doi.org/10.1137/080734030.
  56. Russell Impagliazzo, Valentine Kabanets, and Avi Wigderson. New direct-product testers and 2-query pcps. In Proceedings of the forty-first annual ACM symposium on Theory of computing, pages 131-140, 2009. URL: https://doi.org/10.1145/1536414.1536435.
  57. Fernando Granha Jeronimo, Shashank Srivastava, and Madhur Tulsiani. Near-linear time decoding of ta-shma’s codes via splittable regularity. In Samir Khuller and Virginia Vassilevska Williams, editors, STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21-25, 2021, pages 1527-1536. ACM, 2021. URL: https://doi.org/10.1145/3406325.3451126.
  58. Tali Kaufman, David Kazhdan, and Alexander Lubotzky. Isoperimetric inequalities for ramanujan complexes and topological expanders. Geometric and Functional Analysis, 26(1):250-287, 2016. Google Scholar
  59. Tali Kaufman and David Mass. Local-to-global agreement expansion via the variance method. In Thomas Vidick, editor, 11th Innovations in Theoretical Computer Science Conference, ITCS 2020, January 12-14, 2020, Seattle, Washington, USA, volume 151 of LIPIcs, pages 74:1-74:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ITCS.2020.74.
  60. Tali Kaufman and Izhar Oppenheim. Construction of new local spectral high dimensional expanders. In STOC'18 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, pages 773-786. ACM, New York, 2018. URL: https://doi.org/10.1145/3188745.3188782.
  61. Tali Kaufman and Izhar Oppenheim. Coboundary and cosystolic expansion from strong symmetry. In Nikhil Bansal, Emanuela Merelli, and James Worrell, editors, 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, Glasgow, Scotland (Virtual Conference), July 12-16, 2021, volume 198 of LIPIcs, pages 84:1-84:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPIcs.ICALP.2021.84.
  62. Tali Kaufman and Izhar Oppenheim. High dimensional expansion implies amplified local testability. In Amit Chakrabarti and Chaitanya Swamy, editors, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022, September 19-21, 2022, University of Illinois, Urbana-Champaign, USA (Virtual Conference), volume 245 of LIPIcs, pages 5:1-5:10. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2022.5.
  63. Tali Kaufman, Izhar Oppenheim, and Shmuel Weinberger. Coboundary expansion of coset complexes. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing, pages 1722-1731, 2025. URL: https://doi.org/10.1145/3717823.3718136.
  64. Jonathan Leake, Kasper Lindberg, and Shayan Oveis Gharan. Optimal trickle-down theorems for path complexes via c-lorentzian polynomials with applications to sampling and log-concave sequences. CoRR, abs/2503.01005, 2025. URL: https://doi.org/10.48550/arXiv.2503.01005.
  65. Nathan Linial and Roy Meshulam. Homological connectivity of random 2-complexes. Comb., 26(4):475-487, 2006. URL: https://doi.org/10.1007/s00493-006-0027-9.
  66. Siqi Liu, Sidhanth Mohanty, and Elizabeth Yang. High-dimensional expanders from expanders. In Thomas Vidick, editor, 11th Innovations in Theoretical Computer Science Conference, ITCS 2020, Seattle, Washington, USA, January 12-14, 2020, volume 151 of LIPIcs, pages 12:1-12:32. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. URL: https://doi.org/10.4230/LIPIcs.ITCS.2020.12.
  67. Alexander Lubotzky, Beth Samuels, and Uzi Vishne. Explicit constructions of Ramanujan complexes of type A_d̃. European J. Combin., 26(6):965-993, 2005. URL: https://doi.org/10.1016/j.ejc.2004.06.007.
  68. Or Meir. Combinatorial pcps with short proofs. Comput. Complex., 25(1):1-102, 2016. URL: https://doi.org/10.1007/S00037-015-0111-X.
  69. Dana Moshkovitz and Ran Raz. Two-query pcp with subconstant error. Journal of the ACM (JACM), 57(5):1-29, 2008. Google Scholar
  70. Ryan O'Donnell and Kevin Pratt. High-dimensional expanders from chevalley groups. In Shachar Lovett, editor, 37th Computational Complexity Conference, CCC 2022, Philadelphia, PA, USA, July 20-23, 2022, volume 234 of LIPIcs, pages 18:1-18:26. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.CCC.2022.18.
  71. Ryan O'Donnell and Noah G. Singer. Low-soundness direct-product testers and pcps from kaufman-oppenheim complexes. CoRR, abs/2511.10514, 2025. URL: https://doi.org/10.48550/arXiv.2511.10514.
  72. Izhar Oppenheim. Local spectral expansion approach to high dimensional expanders Part II: Mixing and geometrical overlapping. Discrete Comput. Geom., 64(3):1023-1066, 2020. URL: https://doi.org/10.1007/s00454-019-00117-7.
  73. Pavel Panteleev and Gleb Kalachev. Asymptotically good quantum and locally testable classical LDPC codes. In Stefano Leonardi and Anupam Gupta, editors, STOC '22: 54th Annual ACM SIGACT Symposium on Theory of Computing, Rome, Italy, June 20 - 24, 2022, pages 375-388. ACM, 2022. URL: https://doi.org/10.1145/3519935.3520017.
  74. David B Surowski. Covers of simplicial complexes and applications to geometry. Geometriae Dedicata, 16(1):35-62, 1984. Google Scholar
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