Locally recoverable codes based on the matrices derived from the magic squares

Zengin R., Köroğlu M. E.

9th International IFS and Contemporary Mathematics and Engineering Conference, Mersin, Türkiye, 8 - 11 Temmuz 2023, ss.15

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Mersin
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.15
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

An (n, k, r) locally recoverable code (for shortly LRC) is a code of length n and dimension k over a finite field 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 since they can recover a failed node by accessing the minimum number of the surviving nodes. A matrix is called as 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 by using the magic squares and the parametrization of an LRC code is given by using these (r, t)-regular matrices.