Cyclic $$(r,\delta )$$ locally recoverable codes from their constacyclic and negacyclic subcodes
Year: 2026
Type: article
Abstract: If a symbol in any coordinate of a codeword in a code $$\mathcal {C}$$ can be repaired by accessing at most r other coordinates, then the positive integer r is called locality of the code. Codes with locality are called locally recoverable codes. Locally recoverable codes are preferred in distributed storage systems, such as Microsoft Azure and Hadoop (used by Facebook), due to their ability to recover a failed node by accessing the minimum number of surviving nodes. A code with $$(r,\delta )$$ -locality is a locally recoverable code that allows recovering $$\delta -1$$ erasures simultaneously by reaching at most r other coordinates. In this paper, we obtained constacyclic and negacyclic codes by determining the structure of cyclotomic cosets. Then, we constructed cyclic $$(r,\delta )$$ -LRCs by virtue of their constacyclic and negacyclic subcodes which we found.
Source: Cryptography and Communications
Authors: Rabia Zengin, Mehmet Emin Köroğlu
Institutions: Istanbul Bilgi University, Yıldız Technical University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7150914307