Optimal testing of reed-muller codes

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August undefined, 2024

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A New Upper Bound on the Query Complexity for Testing Generalized Reed …

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 … WebThis leads to a O(d4 d)-query test for degree d Reed-Muller codes. We give an asymptotically optimal analysis of T 0, showing that it rejects functions that are ω(1)-far with ω(1)-probability (so the rejection probability is a universal constant independent of d and n). In particular, this implies that the query complexity of testing degree d ... greene county parks and rec springfield mo

Testing Low-Degree Polynomials over Prime Fields - University …

WebWe 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. WebApr 12, 2024 · By optimal soundness, we mean that if the tester accepts with probability at least (where is small), then it must be the case that is -close to some codeword in Hamming distance. We show that Generalized Reed-Muller codes admit optimal testers with queries. Here, for a prime power , the Generalized Reed-Muller code, RM [n,q,d], consists of the ... WebReed-Muller codes can have smaller q unlike Reed-Solomon, in fact there exist efﬁcient decoding algorithms up to δ 2 and q = 2. The trade off between R and δ however is not that satisfactory as Reed-Muller codes can not have R > 0, δ > 0. Reed-Muller codes have found many uses in complexity theory and codeword testing. Deﬁnition1.1. greene county parks and trail

Almost Optimal Scaling of Reed-Muller Codes on BEC and BSC …

Error Probability Mitigation in Quantum Reading Using Classical Codes

WebWe study affine cartesian codes, which are a Reed-Muller type of evaluation codes, where polynomials are evaluated at the cartesian product of n subsets of a f 掌桥科研一站式科研服务平台 WebThere are exactly two non-equivalent [32,11,12] -codes in the binary Reed-Muller code {\\cal{RM}}(2,5) which contain {\\cal{RM}}(1,5) and have the weight set \\{0,12 ... greene county parks and rec virginiaWebThe following are used throughout the paper: • For nonnegative integers r m, RM(m,r) denotes the Reed-Muller code whose codewords are the evaluation vectors of all multivariate polynomials of degree at most r on m Boolean variables. The maximal degree r is sometimes called the order of the code. greene county parks and rec va

"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 … " - Optimal testing of reed-muller codes

Optimal testing of reed-muller codes

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. 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 …

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WebOver a finite field ${\mathbb{F}}_q$ the (n,d,q)-Reed-Muller code is the code given by evaluations of n-variate polynomials of total degree at most d on all points (of... A New Upper Bound on the Query Complexity for Testing 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 …

WebApr 12, 2024 · Optimal Testing of Generalized Reed-Muller Codes in Fewer Queries. April 2024; License; CC BY 4.0 Weboptimal testing degree polynomial reed-muller code rejection probability 1-query test improved analysis maximal correlation proof work new relationship optimal analysis test showing inverse conjecture classical blum-luby-rubinfeld blr93 linearity test new analysis reed-muller testing problem st-gowers norm

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 … WebThis leads to a O(d 4 d)-query test for degree d Reed-Muller codes. We give an asymptotically optimal analysis of T 0, showing that it rejects functions that are Ω(1)-far …

WebOptimal Testing of Reed-Muller Codes. Authors: Arnab Bhattacharyya. View Profile, Swastik Kopparty. View Profile, Grant Schoenebeck ...

Webcally) 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 ... fluffy eggs in microwaveWebOptimal testing of Reed-Muller codes - IAS. EN. English Deutsch Français Español Português Italiano Român Nederlands Latina Dansk Svenska Norsk Magyar Bahasa Indonesia Türkçe Suomi Latvian Lithuanian česk ... fluffy emailWebWe 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. fluffy emoji headphonesWebOct 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 … fluffyexportWebJun 22, 2024 · This condition applies e.g., to Reed-Mueller codes. Since O(1/N 1/2) is the smallest transition possible for any code, we speak of “almost” optimal scaling. We emphasize that the width of the transition says nothing about the location of the transition. Therefore this result has no bearing on whether a code is capacity-achieving or not. fluffy eggs in the ovenWebThis leads to a O(d4 d)-query test for degree d Reed-Muller codes. We give an asymptotically optimal analysis of T 0, showing that it rejects functions that are ω(1)-far with ω(1) … fluffy exclusiveWebWe 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 … fluffy emo boy hair