Let C be an [n, k, d] GRS code over a finite field F, with 1 d-1. (c) The covering radius of a code C CF is defined to be the largest distance d(y, C) among all y EF. In other words, P(C):= max{dly, C): ye F"}. Part (b) shows that the covering radius of a GRS code of type [n, k, d] is at least d - 1. Prove that it is, in fact, equal to d - 1. [Hint: Show that the covering radius of an MDS code must be strictly less than its minimum distance.] Let C be an [n, k, d] GRS code over a finite field F, with 1 d-1. (c) The covering radius of a code C CF is defined to be the largest distance d(y, C) among all y EF. In other words, P(C):= max{dly, C): ye F"}. Part (b) shows that the covering radius of a GRS code of type [n, k, d] is at least d - 1. Prove that it is, in fact, equal to d - 1. [Hint: Show that the covering radius of an MDS code must be strictly less than its minimum distance.]