Linearized Reed-Solomon Codes and Their Applications

Linearized Reed-Solomon (LRS) codes are a class of evaluation codes based on skew polynomials.  They achieve the Singleton bound in sum-rank metric, which arises in problems of communication over multiplicative-additive matrix channels. In this talk, I will first introduce linearized Reed-Solomon codes and their maximum sum-rank distance seperable (MSRD) property, after reviewing the related properties of skew polynomials, then introduce their applications in distributed storage systems (DSS) as a class of maximally recoverable-locally repairable codes (MR-LRCs).

Outline of the talk

  • Part I: LRS codes and sum-rank metric (~20 mins)
    • Skew polynomials and evaluation
    • Choice of evaluation points to construct LRS codes
    • Sum-rank metric
    • MSRD property of LRS codes
  • Part II: Application in distributed storage system (~25 mins)
    • Maximally recoverable locally repairable codes