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- W2949605300 abstract "Over a finite field $F_q$ 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 $F_q^n$). The task of testing if a function $f:F_q^n to F_q$ is close to a codeword of an $(n,d,q)$-Reed-Muller code has been of central interest in complexity theory and property testing. The query complexity of this task is the minimal number of queries that a tester can make (minimum over all testers of the maximum number of queries over all random choices) while accepting all Reed-Muller codewords and rejecting words that are $delta$-far from the code with probability $Omega(delta)$. (In this work we allow the constant in the $Omega$ to depend on $d$.) In this work we give a new upper bound of $(c q)^{(d+1)/q}$ on the query complexity, where $c$ is a universal constant. In the process we also give new upper bounds on the of the dual of the Reed-Muller code (which is also a Reed-Muller code). The spanning weight of a code is the smallest integer $w$ such that codewords of Hamming weight at most $w$ span the code." @default.
- W2949605300 created "2019-06-27" @default.
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- W2949605300 creator A5053736571 @default.
- W2949605300 date "2012-04-24" @default.
- W2949605300 modified "2023-09-25" @default.
- W2949605300 title "A new upper bound on the query complexity for testing generalized Reed-Muller codes" @default.
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