2016/12/12 by Kathryn Haymaker, Haymaker, Kathryn, Beth Malmskog +3 · 2 citations
Computer Science · #11T71 #14H05 #94B60 #Advanced Data Storage Technologies #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1612.03841
openalex publication_date 2016/12/12 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
We generalize the construction of locally recoverable codes on algebraic curves given by Barg, Tamo and Vlăduţ to those with arbitrarily many recovery sets by exploiting the structure of fiber products of curves. Employing maximal curves, we create several new families of locally recoverable codes with multiple recovery sets, including codes with two recovery sets from the generalized Giulietti and Korchmáros (GK) curves and the Suzuki curves, and new locally recoverable codes with many recovery sets based on the Hermitian curve, using a fiber product construction of van der Geer and van der Vlugt. In addition, we consider the relationship between local error recovery and global error correction as well as the availability required to locally recover any pattern of a fixed number of erasures.