A construction of non-Reed-Solomon type MDS codes
Ron M. Roth, Abraham Lempel · IEEE Transactions on Information Theory · 1989
A construction is presented of long maximum-distance-separable (MDS) codes that are not generalized Reed-Solomon (GRS) type. The construction uses subsets S, mod S mod =m of a finite field F=GF(q) with the property that no t distinct elements of S add up to some fixed element of F. Large subsets of this kind are used to construct (n=m+2, k=t+1) non-GRS MDS codes over F.>