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Let w(n,k) be the largest integer such that there exists a binary group code (n,k) all of whose non-zero elements have weight equal to or larger than w(n,k). In this report values of w(n,k) are given for o< k < or 6 and k < or n < or 100, as well as for o< k < or n < or 24. Further, new upper and lower bounds are obtained which are easy to compute and, in certain regions, better than other known bounds.

Various necessary and sufficient conditions are given for the existence of binary codes with preassigned weights. Some properties of the weight disbution are deduced.