Optimal constacyclic locally recoverable codes with minimum distance 2 and constacyclic codes with minimum locality


Zengin R., Köroğlu M. E.

7th International Researchers, Statisticians, and Young Statisticians Congress, İstanbul, Turkey, 2 - 05 November 2023, pp.98

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.98
  • Yıldız Technical University Affiliated: Yes

Abstract

A locally recoverable code (for brevity LRC) is a code such that a symbol in any coordinate of a codeword can be repaired by using the symbols in at most r other positions. These codes are used in distributed storage systems by Microsoft Azure and Hadoop since they can repair a failed node by accessing the minimum number of the surviving nodes. An LRC which achieves Singleton- type bound is called an optimal LRC. Constacyclic codes are very significant codes because of their efficient encoding and decoding procedures. In this study, we will obtain constacyclic LRCs with minimum locality and optimal constacyclic LRCs with minimum distance 2 from their paritycheck polynomials.