Balanced Sparsest Generator Matrices for MDS Codes

Abstract

We show that given $n$ and $k$, for $q$ sufficiently large, there always exists an $[n,k{]}_q$ MDS code that has a generator matrix $G$ satisfying the following two conditions: (C1) Sparsest: each row of $G$ has Hamming weight $n-k+1$; (C2) Balanced: Hamming weights of the columns of $G$ differ from each other by at most one.

5 pages