Optimal LRC codes for all lenghts n <= q
Oleg Kolosov, Alexander Barg, Itzhak Tamo, Gala Yadgar · arXiv (Cornell University) · 2018
A family of distance-optimal LRC codes from certain subcodes of $q$-ary Reed-Solomon codes, proposed by I.~Tamo and A.~Barg in 2014, assumes that the code length $n$ is a multiple of $r+1.$ By shortening codes from this family, we show that it is possible to lift this assumption, still obtaining distance-optimal codes.