Optimal testing of reed-muller 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... WebJun 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.
Optimal testing of reed-muller codes
Did you know?
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. 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
WebOptimal 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 ... WebApr 12, 2024 · Optimal Testing of Generalized Reed-Muller Codes in Fewer Queries. April 2024; License; CC BY 4.0
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) …
http://www.cse.buffalo.edu/faculty/atri/papers/coding/low_deg_test.pdf
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 … can fish change their genderWeboptimal testing reed-muller code degree polynomial gowers norm 1-query test tight relationship rejection probability alon et optimal analysis reed-muller testing problem st-gowers norm fitbit charge 2 manual guideWebThis 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 … can fish climb treesWebWe 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. can fish come out of shockWeboptimal 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 fitbit charge 2 no touchscreenWebOct 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 … fitbit charge 2 not receiving notificationsWebOptimal Testing of Reed-Muller Codes Abstract: 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 … can fish close their eyes