Optimal LRC codes for all lenghts n <= q

Published 1 Feb 2018 in cs.IT and math.IT | (1802.00157v1)

Abstract: 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.

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