A simplifed proof for the limit of a tower over a cubic finite field

Recently Bezerra, Garcia and Stichtenoth constructed an explicit tower of function fields over a finite field , whose limit attains the Zink bound . Their proof is rather long and very technical. In this paper we replace the complex calculations in their work by structural arguments, thus giving a much simpler and shorter proof for the limit of the Bezerra, Garcia and Stichtenoth tower.