Reed-Solomon codes over small fields with constrained generator matrices

08/20/2018

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by   Gary Greaves, et al.

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We give constructive proofs of the existence 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.