On additive MDS codes with linear projections

Abstract

We support some evidence that a long additive MDS code over a finite field must be equivalent to a linear code. More precisely, let C be an -linear MDS code over . If , , , and C has three coordinates from which its projections are equivalent to -linear codes, we prove that C itself is equivalent to an -linear code. If , , and there are two disjoint subsets of coordinates whose combined size is at most from which the projections of C are equivalent to -linear codes, we prove that C is equivalent to a code which is linear over a larger field than .