The dual geometry of Hermitian two-point codes
  In this paper we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases. 
Edoardo Ballico, Alberto Ravagnani
math.AG