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Reed-Solomon codes over small fields with constrained generator matrices
Gary Greaves, Jeven Syatriadi · 2018-08-20 · via cs.IT updates on arXiv.org

We give constructions of some special cases of $[n,k]$ Reed-Solomon codes over finite fields of size at least $n$ and $n+1$ whose generator matrices have constrained support. Furthermore, we consider a generalisation of the GM-MDS conjecture proposed by Lovett in 2018. We show that Lovett's conjecture is false in general and we specify when the conjecture is true.

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