TL;DR
This paper surveys multiplicity codes, a class of algebraic error-correcting codes that evaluate polynomials and derivatives, highlighting their advantages and open problems.
Contribution
It provides a comprehensive overview of known results, variations, improvements, and open questions related to multiplicity codes.
Findings
Multiplicity codes offer improved local decoding and list-decoding capabilities.
The paper presents variations and enhancements of multiplicity codes.
Several open problems in the theory and application of these codes are identified.
Abstract
Multiplicity codes are algebraic error-correcting codes generalizing classical polynomial evaluation codes, and are based on evaluating polynomials and their derivatives. This small augmentation confers upon them better local decoding, list-decoding and local list-decoding algorithms than their classical counterparts. We survey what is known about these codes, present some variations and improvements, and finally list some interesting open problems.
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