Two classes of locally recoverable codes from cyclic codes with low locality
Computational and Applied Mathematics, vol.46, no.2, 2027 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 46 Issue: 2
- Publication Date: 2027
- Doi Number: 10.1007/s40314-026-03898-9
- Journal Name: Computational and Applied Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: BCH bound, Cyclic codes, Locally recoverable codes
- Yıldız Technical University Affiliated: Yes
Abstract
A code C is said to have locality r if any symbol in a codeword can be reconstructed by referring to no more than r other symbols. These types of codes are referred to as locally recoverable codes (LRCs). Distributed storage systems, such as Microsoft Azure and Hadoop, utilize LRCs due to their ability to recover a failed slot by accessing a small subset of surviving slots, thereby optimizing repair bandwidth and latency. In this study, we construct q-ary cyclic LRCs of lengths u(q+1) and u(q-1) by means of specified defining sets, where q is a prime power and u is a nonnegative integer such that u∣(q-1) and u∣(q+1), respectively. These codes have small locality with respect to the choice of the positive integer u. Notably, some of these codes have locality 1, which represents the minimal possible locality.