The second-order football-pool problem and the optimal rate of generalized-covering codes

The goal of the classic football-pool problem is to determine how many lottery tickets are to be bought in order to guarantee at least n − r correct guesses out of a sequence of n games played. We study a generalized (second-order) version of this problem, in which any of these n games consists of two sub-games. The second-order version of the football-pool problem is formulated using the notion of generalized-covering radius, recently proposed …