Algebraic property testing: the role of invariance
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Locally testable vs. locally decodable codes
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Guest column: testing linear properties: some general theme
ACM SIGACT News
Limitation on the rate of families of locally testable codes
Property testing
Invariance in property testing
Property testing
Limitation on the rate of families of locally testable codes
Property testing
Invariance in property testing
Property testing
Proximity oblivious testing and the role of invariances
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Characterizations of locally testable linear-and affine-invariant families
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
On sums of locally testable affine invariant properties
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Limits on the rate of locally testable affine-invariant codes
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Proximity oblivious testing and the role of invariances
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Characterizations of locally testable linear- and affine-invariant families
Theoretical Computer Science
New affine-invariant codes from lifting
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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A basic goal in Property Testing is to identify a minimal set of features that make a property testable. For the case when the property to be tested is membership in a binary linear error-correcting code, Alon et al.~\cite{AKKLR}had conjectured that the presence of a single low weight code in the dual, and "2-transitivity" of the code (i.e., the code is invariant under a 2-transitive group of permutations on the coordinates of the code) suffice to get local testability. We refute this conjecture by giving a family of error correcting codes where the coordinates of the codewords form a large field of characteristic two, and the code is invariant under affine transformations of the domain. This class of properties was introduced by Kaufman and Sudan~\cite{Kauf-Sudan} as a setting where many results in algebraic property testing generalize. Our result shows a complementary virtue: this family also can be useful in producing counter examples to natural conjectures.