Show that a block code B can detect all patterns of s or fewer errors if and only if d min > s. Show that a block code B can correct all patterns of t or fewer errors and simultaneously detect all...

Show that a block code B can detect all patterns of s or fewer errors if and only if d_min
> s.

Show that a block code B can correct all patterns of t or fewer errors and simultaneously detect all patterns of t + 1, t + 2, . . . , t + s errors if and only if d_min
> 2t + s.