Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Introduction to Coding Theory
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing Low-Degree Polynomials over Prime Fields
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Almost Orthogonal Linear Codes are Locally Testable
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Locally testable codes and PCPs of almost-linear length
Journal of the ACM (JACM)
Testing Polynomials over General Fields
SIAM Journal on Computing
Sparse Random Linear Codes are Locally Decodable and Testable
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Algebraic property testing: the role of invariance
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Long extended BCH codes are spanned by minimum weight words
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
IEEE Transactions on Information Theory
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
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
New affine-invariant codes from lifting
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
A new family of locally correctable codes based on degree-lifted algebraic geometry codes
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Motivated by questions in property testing, we search for linear error-correcting codes that have the "single local orbit" property: they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every "sparse" binary code whose coordinates are indexed by elements of for prime n , and whose symmetry group includes the group of non-singular affine transformations of , has the single local orbit property. (A code is sparse if it contains polynomially many codewords in its block length.) In particular this class includes the dual-BCH codes for whose duals (BCH codes) simple bases were not known. Our result gives the first short (O (n )-bit, as opposed to $\exp(n)$-bit) description of a low-weight basis for BCH codes. If 2 n *** 1 is a Mersenne prime, then we get that every sparse cyclic code also has the single local orbit.