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Local decoding and testing of polynomials over grids

2020
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Random structures & algorithms (Print)
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The well-known DeMillo-Lipton-Schwartz-Zippel lemma says that n-variate polynomials of total degree at most d over grids, i.e. sets of the form A 1 ×A 2 ×· · ·×A n , form error-correcting codes (of distance at least 2 −d provided min i {|A i |} ≥ 2). In this work we explore their local decodability and local testability. While these aspects have been studied extensively when A 1 = · · · = A n = F q are the same finite field, the setting when A i 's are not the full field does not seem to have

doi:10.1002/rsa.20933
fatcat:wrtcbryhf5caxd3kjoucjkssdq