Binary Locally Recoverable Codes Based on Matrices Derived from Cyclotomic Cosets


Zengin R., Köroğlu M. E.

15th International Conference on Algebraic Hyperstructures and its Applications (AHA2023), İstanbul, Turkey, 28 - 30 July 2023, pp.56

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.56
  • Yıldız Technical University Affiliated: Yes

Abstract

A binary (n, k,r) locally recoverable code is a binary code of length n and dimension k over finite field F_2 such that a symbol in any coordinate of a codeword can be recovered by accessing the symbols in at most r other coordinates.These codes are used in distributed storage systems by Microsoft Azure and Hadoop today thanks to they can recover a failed node by accessing the minimum number of the survivingn odes. A matrix is called an (r, t)-regular matrix if its each row has uniform weight r and each column has uniform weight t. In this study,new(r, t)-regular matrices are obtained from cyclotomic cosets and parameters of an LRC are given by using these (r, t)-regular matrices.Furthermore, the condition of being optimal for these codes is explained.