The Mexican Roll takes its name from Tony Rihan. Tony is a Mexican Tasty trader and was the first to describe this type of roll. You can read about his trade strategies here.
The Mexican Roll is a dynamic strategy. It consist of rolling out to the next period (you may specify 30, 40 days out) and reduce the risk at the same time. The algorithm will dynamically identify the strike(s) that meet both criteria lower delta, and positive premium return. ,The premium condition is to be positive but as close to zero as possible.