On the second greedy weight for linear codes of dimension at least 4

The maximum of g/sub 2/ - d/sub 2/ for linear [n,k,d;q] codes C is studied. Here d/sub 2/ is the smallest size of the support of a two-dimensional subcode of C and g/sub 2/ is the smallest size of the support of a two-dimensional subcode of C which contains a codeword of weight d. For codes of dimension 4 or more, upper and lower bounds on the maximum of g/sub 2/-d/sub 2/ are given.