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 … 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 …

CiteSeerX — Optimal Testing of Reed-Muller Codes

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). 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 ... how many primos from daily commissions

Optimal testing of Reed-Muller codes

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 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 … 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)-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 ... how could i break an angels wings song