Optimal testing of reed-muller codes
http://www.cse.buffalo.edu/faculty/atri/papers/coding/low_deg_test.pdf
Optimal testing of reed-muller codes
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WebReed-Muller codes (over both large and small nite elds) have been extremely in uential ... [BGH+12], which uses the optimal testing result of [BKS+10]. And the list goes on. Needless to say, the properties used in these works are properties of low-degree polynomials (such WebOur methods are more general and also allow us to prove that a wide class of testers, which follow the form of the Ron-Zewi and Sudan tester, are optimal. This result applies to testers for all affine-invariant codes (which are not necessarily generalized Reed-Muller codes).
Web1.1 Reed-Muller Codes and Testing The Reed-Muller codes are parameterized by two parameters: nthe number of variables and dthe degree parameter. The Reed-Muller … WebThis section introduces the main concepts of classical codes and quantum reading needed for this paper. We begin with a brief overview of cyclic codes and then specialize in Reed–Solomon and BCH codes. Subsequently, we show a construction method for Reed–Muller codes that is similar to Reed–Solomon codes.
WebOct 4, 2009 · Alon et al. [AKK+05] proposed and analyzed a natural 2d + 1-query test T 0, and showed that it accepts every degree d polynomial with probability 1, while rejecting functions that are Ω (1)-far... WebAlon et al. [AKK+05] proposed and analyzed a natural 2 d+1-query test T 0, and showed that it accepts every degree d polynomial with probability 1, while rejecting functions that are …
WebThe Reed-Muller codes are parameterized by two parameters: nthe number of variables and dthe degree parameter. The Reed-Muller codes consist of all functions from Fn 2!F 2that …
WebAbstract. We consider the problem of testing if a given function f: F 2 n → F 2 is close to any degree d polynomial in n variables, also known as the Reed-Muller testing problem. Alon et al. [AKKLR] proposed and analyzed a natural 2 d+1-query test for this property and showed that it accepts every degree d polynomial with probability 1, while rejecting functions that … consall shootWebquery test for this task. In this work we give an improved, asymptotically optimal, analysis of their test. Below we describe the problem, its context, our results and some implications. … consall occinvestment on bank statementWebOur question is also called testing of Reed-Muller codes, which are codes based on low-degree polynomials. The Reed-Muller codes are parameterized by two parameters: n, the … editing eaglesWebWe consider the problem of testing if a given function f : double-struck F 2 n → double-struck F 2 is close to any degree d polynomial in n variables, also known as the Reed-Muller testing problem. Alon et al. [1] proposed and analyzed a natural 2 d+1-query test for this problem.This test turned out to be intimately related to the Gowers norm. consall team kftWebWe consider the problem of testing if a given function f : double-struck F 2 n → double-struck F 2 is close to any degree d polynomial in n variables, also known as the Reed-Muller testing problem. Alon et al. [1] proposed and analyzed a natural 2 d+1-query test for this problem.This test turned out to be intimately related to the Gowers norm. consall woods rspbWeb1.5.1 Optimal Testing of Reed-Muller Codes via Global Hypercontractivity In [31], the authors relate the analysis of the t-flat tester of the Reed-Muller code to expansion properties of the affine Grassmann graph. Here, the affine Grassmann graph is the graph whose vertex set is the set of all t-flats in Fn editing early modern texts hunterWebcally) testing Reed-Muller codes. Their strategy is then to pick a random minimum-weight codeword from the dual code and to check if it is orthogonal to the tested vector. It is important to note that these minimum-weight code words generate the Reed-Muller code. Specifically their test works as follows: given a function f : f0;1gn! f0;1g, to ... cons about shopping at hobby lobby