Constacyclic codes with locality at most 2 and dimension 2

Zengin R., Köroğlu M. E.

7th International Researchers, Statisticians, and Young Statisticians Congress, İstanbul, Turkey, 2 - 05 November 2023, pp.46

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.46
  • Yıldız Technical University Affiliated: Yes


Locally recoverable codes (for short LRCs) are codes such that a symbol in any coordinate of a codeword can be repaired by accessing the symbols in at most r other coordinates. The distributed storage systems by Microsoft Azure and Hadoop uses such codes since they can recover a failed node by accessing the minimum number of the surviving nodes. Constacyclic codes have a wide range of uses in consumer electronics because of their cost-effective encoding and decoding procedures. Here, we have obtained constacyclic LRCs with dimension 2 and locality at most 2. We have proved a necessary and sufficient condition for constacyclic codes with locality 1 which is minimum. Then we have generalized the construction for constacyclic LRCs with any dimension and locality.