Optimal testing of reed-muller codes
Web2 Reed-Muller Codes and Testing The Reed-Muller codes are parameterized by two parameters: n the number of variables and d the degree parameter. The Reed-Muller … 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 …
Optimal testing of reed-muller codes
Did you know?
Webquery 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. … 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 ...
WebApr 12, 2024 · Optimal Testing of Generalized Reed-Muller Codes in Fewer Queries. April 2024; License; CC BY 4.0 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
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 … 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).
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 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. busy bs bridalWebOur 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 … busy brush cafe wallingfordWebOver 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 … busy b stickersWebReed-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. busy bs cleaning services canton txWeboptimal 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 busy b travel wallet 14.90 amazonWebThis 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 ... ccog women\\u0027s health groupWebOptimal 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 … ccog women\u0027s health group