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Balanced Sparsest Generator Matrices for MDS Codes (1301.5108v1)
Published 22 Jan 2013 in cs.IT and math.IT
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.