Near-MDS Codes from Maximal Arcs in PG$(2,q)$

Li Xu, Cuiling Fan, Dongchun Han

The singleton defect of an $[n,k,d]$ linear code $\mathcal{C}$ is defined as $s(\mathcal{C})=n-k+1-d$. Codes with $S(\mathcal{C})=0$ are called maximum distance separable (MDS) codes, and c…