Decoding Downset codes over a finite grid
Computational Complexity
2019-08-21 v1 Combinatorics
Abstract
In a recent paper, Kim and Kopparty (Theory of Computing, 2017) gave a deterministic algorithm for the unique decoding problem for polynomials of bounded total degree over a general grid. 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.
Cite
@article{arxiv.1908.07215,
title = {Decoding Downset codes over a finite grid},
author = {Srikanth Srinivasan and Utkarsh Tripathi and S. Venkitesh},
journal= {arXiv preprint arXiv:1908.07215},
year = {2019}
}