Locally Recoverable Codes with Availability t≥ 2 from Fiber Products of Curves [article]

Kathryn Haymaker, Beth Malmskog, Gretchen Matthews
2018 arXiv   pre-print
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
more » ... 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.
arXiv:1612.03841v4 fatcat:ansbd35nm5ah3lt24bieob3a7y