Some remarks on multiplicity codes

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.Comment: 21 pages in Discrete Geometry and Algebraic Combinatorics, AMS Contemporary Mathematics Series, 201