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→Limits: Edited reference to include links on author names Irit Dinur.Shai Evra, Ron Livne, Alexander Lubotzky, Shahar Mozes |
Edited from "a preprint has reported" to "two preprints have reported" to include work of Pavel Panteleev and Gleb Kalachev |
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The next nearly linear goal is linear up to a [[polylogarithmic]] factor; <math>n=\text{poly}(\log k)*k</math>. Nobody has yet to come up with a linearly testable code that satisfies this constraint.<ref name=shortLTC/>
In November 2021 two preprints have reported<ref>{{Cite journal|last=Panteleev|first=Pavel|last2=Kalachev|first2=Gleb|date=2021-11-05|title=Asymptotically Good Quantum and Locally Testable Classical LDPC Codes|url=http://arxiv.org/abs/2111.03654|journal=arXiv:2111.03654 [quant-ph]}}</ref><ref>{{Cite journal|last=Dinur|first=Irit|author-link=Irit Dinur|last2=Evra|first2=Shai|author-link2=Shai Evra|last3=Livne|first3=Ron|last4=Lubotzky|first4=Alexander|author-link4=Alexander Lubotzky|last5=Mozes|first5=Shahar|author-link5=Shahar Mozes|date=2021-11-08|title=Locally Testable Codes with constant rate, distance, and locality|url=http://arxiv.org/abs/2111.04808|journal=arXiv:2111.04808 [cs, math]}}</ref><ref>{{Cite web|last=Rorvig|first=Mordechai|date=2021-11-24|title=Researchers Defeat Randomness to Create Ideal Code|url=https://www.quantamagazine.org/researchers-defeat-randomness-to-create-ideal-code-20211124/|url-status=live|access-date=2021-11-24|website=[[Quanta Magazine]]|language=en}}</ref> the first polynomial-time construction of "<math>c^3</math>-LTCs" namely locally testable codes with constant rate <math>r</math>, constant distance <math>\delta</math> and constant locality <math>q</math>.
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