On the second greedy weight for linear codes of dimension at least 4
The maximum of g(2) - d(2) for linear [n, k, d; q] codes C is studied. Here d(2) is the smallest size of the support of a two-dimensional subcode of C and g(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(2) - d(2) are given.
greedy weight support bounds constructions generalized hamming weight