文章基本信息

标题：Sparse affine-invariant linear codes are locally testable
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作者：Eli Ben-Sasson ; Noga Ron-Zewi ; Madhu Sudan 等
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2012
卷号：2012
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We show that sparse affine-invariant linear properties over arbitrary finite fields are locally testable with a constant number of queries. Given a finite field Fq and an extension field Fqn, a property is a set of functions mapping Fqn to Fq. The property is said to be affine-invariant if it is invariant under affine transformations of Fqn, and it is said to be sparse if its size is polynomial in the domain size. Our work completes a line of work initiated by Grigorescu et al. [RANDOM 2009] and followed by Kaufman and Lovett [FOCS 2011]. The latter showed such a result for the case when q was prime. Extending to non-prime cases turns out to be non-trivial and our proof involves some detours into additive combinatorics, as well as a new calculus for building property testers for affine-invariant linear properties.
关键词：affine invariance, finite fields, Locally testable codes, Reed Muller codes