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. 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 …

Optimal Testing of Generalized Reed-Muller Codes in Fewer Queries

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). 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. 単4 単3 違い

Optimal Testing of Reed-Muller Codes - typeset.io

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. WebWe consider the problem of testing if a given function $f : \\F_2^n \\right arrow \\F_2$ is close to any degree $d$ polynomial in $n$ variables, also known as the ... 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 ... 単4ledライト