@article{gopi2020improved,
author = {Gopi, Sivakanth and Guruswami, Venkatesan},
title = {Improved Maximally Recoverable LRCs using Skew Polynomials},
year = {2020},
month = {December},
abstract = {An (n,r,h,a,q)-LRC is a linear code over F_q of length n, whose codeword symbols are partitioned into n/r local groups each of size r. Each local group satisfies 'a' local parity checks to recover from 'a' erasures in that local group and there are further h global parity checks to provide fault tolerance from more global erasure patterns. Such an LRC is Maximally Recoverable (MR), if it can correct all erasure patterns which are information-theoretically correctable given this structure---these are precisely patterns with up to 'a' erasures in each local group and an additional h erasures anywhere in the codeword.

We give an explicit construction of (n,r,h,a,q)-MR LRCs with field size q bounded by max[r,n/r]^[min[h,r-a]]. This significantly improves upon known constructions in most parameter ranges. Moreover, it matches the best known lower bound in an interesting range of parameters where r ~ sqrt[n], r-a ~ sqrt[n]) and h is a fixed constant with h<= a+2, achieving the optimal field size of  ~ n^[h/2]. Our construction is based on the theory of skew polynomials.},
url = {http://approjects.co.za/?big=en-us/research/publication/improved-maximally-recoverable-lrcs-using-skew-polynomials/},
journal = {IEEE Transactions on Information Theory},
}