Optimum Linear Codes with Support Constraints over Small Fields
Hikmet Yıldız, Babak Hassibi · 2018
We consider the problem of designing optimal linear codes (in terms of having the largest minimum distance) subject to a support constraint on the generator matrix. We show that the largest minimum distance can be achieved by a subcode of a Reed-Solomon code of small field size and with the same minimum distance. As a by-product of this result, we settle the GM-MDS conjecture of Dau et al. in the affirmative.