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Information Theory and Coding by Example by Yuri Suhov, Mark Kelbert

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Solution (a) An MDS [N,k,d] code has d = N k + 1. If a linear code image has d{image) = d then any (d – 1) columns of its parity-check matrix H are linearly independent, and (d − 1) is the maximal number with this property, and vice versa. So, any (N k) columns are linearly independent and (N − k) is the maximal such number, and vice versa. Equivalently, any (N k) × (N k) submatrix of H is invertible.

(b) Let image be [N, k, d] MDS code with a parity-check ...

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