A Matrix Completion Approach to Linear Index Coding Problem
  In this paper, a general algorithm is proposed for rate analysis and code design of linear index coding problems. Specifically a solution for minimum rank matrix completion problem over finite fields representing the linear index coding problem is devised in order to find the optimum transmission rate given vector length and size of the field. The new approach can be applied to both scalar and vector linear index coding. 
Homa Esfahanizadeh, Farshad Lahouti, Babak Hassibi
cs.IT math.IT