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ECCC
2011
2011
Dense locally testable codes cannot have constant rate and distance
A q-query locally testable code (LTC) is an error correcting code that can be tested by a randomized algorithm that reads at most q symbols from the given word. An important question is whether there exist LTCs that have the c3 property: constant rate, constant relative distance, and that can be tested with a constant number of queries. Such LTCs are sometimes referred to as “asymptotically good”. We show that dense LTCs cannot be c3 . The density of a tester is roughly the average number of distinct local views in which a coordinate participates. An LTC is dense if it has a tester with density ω(1). More precisely, we show that a 3-query locally testable code with a tester of density ω(1) cannot be c3 . Furthermore, we show that a q-locally testable code (q > 3) with a tester of density ω(1)nq−2 cannot be c3 . Our results hold when the tester has the following two properties: – (no weights:) Every q-tuple of queries occurs with the same probability. – (‘last-one-fix...
Real-time Traffic| Added | 27 Aug 2011 |
| Updated | 27 Aug 2011 |
| Type | Journal |
| Year | 2011 |
| Where | ECCC |
| Authors | Irit Dinur, Tali Kaufman |
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