Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Succinct Representation of Codes with Applications to Testing
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Approximating the distance to monotonicity in high dimensions
ACM Transactions on Algorithms (TALG)
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
Testing linear-invariant non-linear properties: a short report
Property testing
Limitation on the rate of families of locally testable codes
Property testing
Invariance in property testing
Property testing
Testing linear-invariant non-linear properties: a short report
Property testing
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
Hard functions for low-degree polynomials over prime fields
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Symmetric functions capture general functions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
The quantum query complexity of learning multilinear polynomials
Information Processing Letters
New affine-invariant codes from lifting
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Every locally characterized affine-invariant property is testable
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Hard Functions for Low-Degree Polynomials over Prime Fields
ACM Transactions on Computation Theory (TOCT)
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In this work we fill the knowledge gap concerning testing polynomials over finite fields. As previous works show, when the cardinality of the field, $q$, is sufficiently larger than the degree bound, $d$, then the number of queries sufficient for testing is polynomial or even linear in $d$. On the other hand, when $q=2$ then the number of queries, both sufficient and necessary, grows exponentially with $d$. Here we study the intermediate case where $2 generalized Reed-Muller (GRM) codes) are locally testable. In the course of our analysis we provide a characterization of small-weight words that span the code. Such a characterization was previously known only when the field size is a prime or is sufficiently large, in which case the minimum-weight words span the code.