On Walsh code assignment
  The paper considers the problem of orthogonal variable spreading Walsh-code assignments. The aim of the paper is to provide assignments that can avoid both complicated signaling from the BS to the users and blind rate and code detection amongst a great number of possible codes. The assignments considered here use a partition of all users into several pools. Each pool can use its own codes that are different for different pools. Each user has only a few codes assigned to it within the pool. We state the problem as a combinatorial one expressed in terms of a binary n x k matrix M where is the number n of users, and k is the number of Walsh codes in the pool. A solution to the problem is given as a construction of M, which has the assignment property defined in the paper. Two constructions of such M are presented under different conditions on n and k. The first construction is optimal in the sense that it gives the minimal number of Walsh codes assigned to each user for given n and k. The optimality follows from a proved necessary condition for the existence of M with the assignment property. In addition, we propose a simple algorithm of optimal assignment for the first construction. 
B.S.Tsybakov and A.B.Tsybakov
cs.IT math.IT