Information Sets of Multiplicity Codes
This work addresses an incremental improvement in coding theory by validating and extending a known construction for Multiplicity codes.
The paper tackles the problem of systematic encoding for Multiplicity codes by properly defining information sets and providing detailed proofs using generating functions, resulting in a complexity estimate for the encoding algorithm.
We here provide a method for systematic encoding of the Multiplicity codes introduced by Kopparty, Saraf and Yekhanin in 2011. The construction is built on an idea of Kop-party. We properly define information sets for these codes and give detailed proofs of the validity of Kopparty's construction, that use generating functions. We also give a complexity estimate of the associated encoding algorithm.