Lower bounds for Locally Correctable Codes over fields of characteristic zero

Error correcting codes are ubiquitous in computer science, both in theory and in practice. In recent years there has been growing interest in constructing error correcting codes which have local properties, as these codes can be used to safely store large amounts of data, while enabling users to efficiently recover small amounts of data without querying the entire codeword. Despite much progress made in the construction of error correcting codes with high rate and distance, many challenges still remain on whether such powerful codes exist with the additional local properties mentioned above.

The goal of this project is to prove that error correcting codes which have the ability of being locally corrected cannot have high rate and distance, when the base field is of characteristic zero.

Prerequisites

The ideal URA should have a solid command of:

  • linear algebra (equivalent of MATH 245, or MATH 235),
  • basic abstract algebra (such as the material from PMATH 347),
  • coding theory

Applying

If you are interested and have the prerequisites for this project, please send me the following by email:

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Rafael Oliveira
Rafael Oliveira
Assistant Professor of Computer Science

My research interests include complexity theory, algebra, algebraic geometry, commutative algebra, invariant theory, representation theory, derandomization.