ON THE SECOND GREEDY WEIGHT FOR LINEAR CODES SATISFYING THE FULLRANK CONDITION

摘要

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 2-dimensional subcodes of C and g_2 is the smallest size of the support of 2-dimensional subcodes of C which contains a codeword of weight d. The extra cost to the greedy adversary to get two symbols of information using some algorithm is g_2 ― d_2. For codes satisfying the fullrank condition of general dimensions, upper bounds on the maximum of g_2 ― d_2 are given. Under some condition we have got code C where g_2 ― d_2 reaches the upper bound.