3 Search Results for "Viderman, Michael"

Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.59
Testing Tensor Products of Algebraic Codes

Authors: Sumegha Garg, Madhu Sudan, and Gabriel Wu

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
Motivated by recent advances in locally testable codes and quantum LDPCs based on robust testability of tensor product codes, we explore the local testability of tensor products of (an abstraction of) algebraic geometry codes. Such codes are parameterized by, in addition to standard parameters such as block length n and dimension k, their genus g. We show that the tensor product of two algebraic geometry codes is robustly locally testable provided n = Ω((k+g)²). Apart from Reed-Solomon codes, this seems to be the first explicit family of two-wise tensor codes of high dual distance that is robustly locally testable by the natural test that measures the expected distance of a random row/column from the underlying code.
Cite as

Sumegha Garg, Madhu Sudan, and Gabriel Wu. Testing Tensor Products of Algebraic Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 59:1-59:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{garg_et_al:LIPIcs.APPROX/RANDOM.2025.59,
  author =	{Garg, Sumegha and Sudan, Madhu and Wu, Gabriel},
  title =	{{Testing Tensor Products of Algebraic Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{59:1--59:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.59},
  URN =		{urn:nbn:de:0030-drops-244254},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.59},
  annote =	{Keywords: Algebraic geometry codes, Robust testability, Tensor products of codes}
}
Document
DOI: 10.4230/LIPIcs.CCC.2025.25
Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products

Authors: Louis Golowich and Venkatesan Guruswami

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract
The first linear-distance quantum LDPC codes were recently constructed by a line of breakthrough works (culminating in the result of Panteleev & Kalachev, 2021). All such constructions, even when allowing for almost-linear distance, are based on an operation called a balanced (or lifted) product, which is used in a one-shot manner to combine a pair of large classical codes possessing a group symmetry. We present a new construction of almost-linear distance quantum LDPC codes that is iterative in nature. Our construction is based on a more basic and widely used product, namely the homological product (i.e. the tensor product of chain complexes). Specifically, for every ε > 0, we obtain a family of [[N,N^{1-ε},N^{1-ε}]] (subsystem) quantum LDPC codes via repeated homological products of a constant-sized quantum locally testable code. Our key idea is to remove certain low-weight codewords using subsystem codes (while still maintaining constant stabilizer weight), in order to circumvent a particular obstruction that limited the distance of many prior homological product code constructions to at most Õ(√N).
Cite as

Louis Golowich and Venkatesan Guruswami. Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 25:1-25:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{golowich_et_al:LIPIcs.CCC.2025.25,
  author =	{Golowich, Louis and Guruswami, Venkatesan},
  title =	{{Quantum LDPC Codes of Almost Linear Distance via Iterated Homological Products}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{25:1--25:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.25},
  URN =		{urn:nbn:de:0030-drops-237196},
  doi =		{10.4230/LIPIcs.CCC.2025.25},
  annote =	{Keywords: Quantum Error Correction, Quantum LDPC Code, Homological Product, Iterative Construction}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.58
Explicit Strong LTCs with Inverse Poly-Log Rate and Constant Soundness

Authors: Michael Viderman

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
An error-correcting code C subseteq F^n is called (q,epsilon)-strong locally testable code (LTC) if there exists a tester that makes at most q queries to the input word. This tester accepts all codewords with probability 1 and rejects all non-codewords x not in C with probability at least epsilon * delta(x,C), where delta(x,C) denotes the relative Hamming distance between the word x and the code C. The parameter q is called the query complexity and the parameter epsilon is called soundness. Goldreich and Sudan (J.ACM 2006) asked about the existence of strong LTCs with constant query complexity, constant relative distance, constant soundness and inverse polylogarithmic rate. They also asked about the explicit constructions of these codes. Strong LTCs with the required range of parameters were obtained recently in the works of Viderman (CCC 2013, FOCS 2013) based on the papers of Meir (SICOMP 2009) and Dinur (J.ACM 2007). However, the construction of these codes was probabilistic. In this work we show that codes presented in the works of Dinur (J.ACM 2007) and Ben-Sasson and Sudan (SICOMP 2005) provide the explicit construction of strong LTCs with the above range of parameters. Previously, such codes were proven to be weak LTCs. Using the results of Viderman (CCC 2013, FOCS 2013) we prove that such codes are, in fact, strong LTCs.
Cite as

Michael Viderman. Explicit Strong LTCs with Inverse Poly-Log Rate and Constant Soundness. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{viderman:LIPIcs.APPROX-RANDOM.2018.58,
  author =	{Viderman, Michael},
  title =	{{Explicit Strong LTCs with Inverse Poly-Log Rate and Constant Soundness}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{58:1--58:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.58},
  URN =		{urn:nbn:de:0030-drops-94620},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.58},
  annote =	{Keywords: Error-Correcting Codes, Tensor Products, Locally Testable Codes}
}
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