Good Locally Testable Codes
Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, Shahar Mozes
TL;DR
This paper presents an explicit construction of locally testable codes that maintain constant rate, distance, and query complexity, solving a longstanding problem in coding theory.
Contribution
It provides the first explicit construction of such codes with constant parameters, advancing the understanding of locally testable codes.
Findings
Constructed codes have constant rate, distance, and query complexity.
Solved the $c^3$-problem affirmatively.
Demonstrated the existence of efficient locally testable codes.
Abstract
An explicit construction of locally testable codes of constant rate, constant distance and constant number of queries is given. Hence answering affirmatively the -problem.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · graph theory and CDMA systems · Coding theory and cryptography