Optimal testing of reed-muller codes
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 ... 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
Optimal testing of reed-muller codes
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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 … WebOur 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 …
WebOptimal Testing of Reed-Muller Codes. Authors: Arnab Bhattacharyya. View Profile, Swastik Kopparty. View Profile, Grant Schoenebeck ... WebThe 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.
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 … 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 …
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).
WebOptimal Testing of Reed-Muller Codes Pages 488–497 ABSTRACT Index Terms Comments ABSTRACT We consider the problem of testing if a given function $f : \F_2^n \right arrow … cannot access parent profile on fire 7 kidsWeboptimal 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 cannot access pc on networkWeb1.5.1 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 fizzy alcoholic drink crossword climberWebOct 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... cannot access props before initializationWebcally) 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 ... fizzy among usWebThis 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. cannot access public folder codeigniterWebApr 12, 2024 · Optimal Testing of Generalized Reed-Muller Codes in Fewer Queries. April 2024; License; CC BY 4.0 fizzy apple cider wow