Trivariate Lifted Codes with Disjoint Repair Groups

摘要

Guo, Kopparty, and Sudan introduced the notion of lifted Reed-Solomon codes in the context of locally correctable codes. We continue the study of lifted codes with the application for so-called t-disjoint-repair-group property (t-DRGP) codes. A code is said to have the t-DRGP if every symbol in a codeword from the code has t mutually disjoint recovering sets of coordinates in the codeword. In some parameter regimes, our proposed t-DRGP codes based on lifted codes have lower redundancy than previously known t-DRGP codes.