I. Introduction
Designing error-correcting codes with support-constrained generator matrices is motivated by its application in network coding for wireless cooperative data exchange [1], wireless sensor networks [2] and multiple access networks [3]. From both, the theoretical and the practical point of view, the objective is to design codes with support-constrained generator matrix achieving the maximum minimum distance. In Hamming metric, research has been done in developing and proving necessary and sufficient conditions such that there exists an MDS code fulfilling the support constraints. It was first conjectured in [4], referred as the GM–MDS conjecture, and finally proven by Yildiz and Hassibi [5] and independently by Lovett [6].