If we have an $(n,k)$ MDS code and we take a subset of coordinates in a set say $J$, where $|J| > k$. If $c$ is a codeword in the original MDS code let $c_J$ denote its projection on the set $J$. Is it true that set of codewords $\{c_J \}$ is also an MDS code? Is there an easy reference for this? Is there a similar results for maximum rank distance (aka MRD) codes by Gabidulin?
2026-03-26 01:00:24.1774486824
Restricting an MDS code to a subset of coordinates
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