*Solution *(a) An MDS [*N*,*k*,*d*] code has *d *= *N *– *k* + 1. If a linear code has *d*{) = *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 be [*N*, *k*, *d*] MDS code with a parity-check ...

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