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Testing and Weight Distributions of Dual Codes
- Theoretical Computer Science
, 1997
"... We study the testing problem, that is, the problem of determining (maybe probabilistically) if a function to which we have oracle access satisfies a given property. We propose a framework in which to formulate and carry out the analyzes of several known tests. This framework establishes a connection ..."
Abstract
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We study the testing problem, that is, the problem of determining (maybe probabilistically) if a function to which we have oracle access satisfies a given property. We propose a framework in which to formulate and carry out the analyzes of several known tests. This framework establishes a connection between testing and the theory of weight distributions of dual codes. We illustrate this connection by giving a coding theoretic interpretation of several tests that fall under the label of low-degree tests. We also show how the coding theoretic connection we establish naturally suggests a new way of testing for linearity over finite fields. There are two important parameters associated to every test. The first one is the test's probability of rejecting the claim that the function to which it has oracle access satisfies a given property. The second one is the distance from the oracle function to any function that satisfies the property of interest. The goal when analyzing tests is to explai...
