  We consider redundant binary joint digital expansions of integer vectors. The
redundancy is used to minimize the Hamming weight, i.e., the number of nonzero
digit vectors. This leads to efficient linear combination algorithms in abelian
groups, which are for instance used in elliptic curve cryptography.
  If the digit set is a set of contiguous integers containing the zero, a
special syntactical condition is known to minimize the weight. We analyze the
optimal weight of all non-negative integer vectors with maximum entry less than
N. The expectation and the variance are given with a main term and a periodic
fluctuation in the second order term. Finally, we prove asymptotic normality.
