List decoding of a class of affine variety codes
Olav Geil, Casper Thomsen

TL;DR
This paper improves bounds on the zeros of multivariate polynomials over finite sets and applies these results to develop an enhanced list decoding algorithm for affine variety codes.
Contribution
It introduces new bounds on polynomial zeros and leverages them to create a more effective list decoding method for affine variety codes.
Findings
Derived improved bounds on the number of zeros of multivariate polynomials
Designed a list decoding algorithm with better performance for affine variety codes
Enhanced decoding capability for a broad class of affine variety codes
Abstract
Consider a polynomial in variables and a finite point ensemble . When given the leading monomial of with respect to a lexicographic ordering we derive improved information on the possible number of zeros of of multiplicity at least from . We then use this information to design a list decoding algorithm for a large class of affine variety codes.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cellular Automata and Applications
