Improved erasure list decoding locally repairable codes using alphabet-dependent list recovery

New optimal constructions of locally repairable codes over small fields and their polynomial-time erasure list decoding are considered. Our code constructions are based on generalized code concatenation and give optimal binary codes with locality r = 2; 3. The impact of alphabet-dependent list recovery for alternant codes when applied to erasure list decoding of our constructed binary locally repairable codes is analyzed.