WebReed-Muller codes (over both large and small nite elds) have been extremely in uential ... [BGH+12], which uses the optimal testing result of [BKS+10]. And the list goes on. Needless to say, the properties used in these works are properties of low-degree polynomials (such 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 ...
A New Upper Bound on the Query Complexity for Testing Generalized Reed …
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 … 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 … detergent to wash colors and whites together
(PDF) Optimal Testing of Reed-Muller Codes - ResearchGate
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 … 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. 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 ... detergent to use in pressure washer