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arxiv: 1301.5108 · v1 · pith:QWYDOWS2new · submitted 2013-01-22 · 💻 cs.IT · math.IT

Balanced Sparsest Generator Matrices for MDS Codes

Son Hoang Dau , Wentu Song , Zheng Dong , Chau Yuen This is my paper
classification 💻 cs.IT math.IT
keywords balancedgeneratorhammingsparsestalwayscodecodescolumns
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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.

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