Information Sets of Multiplicity Codes
Daniel Augot (GRACE), Fran\c{c}oise Levy-Dit-Vehel (ENSTA ParisTech, UMA), Man Cuong Ng\^o (GRACE)
TL;DR
This paper introduces a systematic encoding method for Multiplicity codes, defining their information sets and providing proofs and complexity estimates for the encoding process.
Contribution
It offers a new systematic encoding approach for Multiplicity codes, including formal definitions, validation proofs, and complexity analysis.
Findings
Validated the construction of information sets for Multiplicity codes
Provided detailed proofs using generating functions
Estimated the encoding algorithm's complexity
Abstract
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.
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Taxonomy
TopicsCoding theory and cryptography · Cellular Automata and Applications · Error Correcting Code Techniques