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Decoding Variants of Reed-Muller Codes over Finite Grids

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Published:08 November 2020Publication History
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Abstract

In a recent article, Kim and Kopparty (2017) gave a deterministic algorithm for the unique decoding problem for polynomials of bounded total degree over a general grid S1 × … × Sm. We show that their algorithm can be adapted to solve the unique decoding problem for the general family of Downset codes. Here, a downset code is specified by a family D of monomials closed under taking factors: The corresponding code is the space of evaluations of all polynomials that can be written as linear combinations of monomials from D.

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