On The Second Relative Greedy Weight And The T-wise Intersection Of Relative Three-weight Codes

Based on the wire-tap channel of type II with two users given by Luo et al in 2005,we introduce the relative greedy weights. A finite projective geometry method is presented in order to describe the relative greedy weights. By using this finite projective geometry method, the optimal 3-dimensional q-ary codes are searched so as to maximize the effort for the adversary to obtain the second data symbol on condition that he has obtained the first data symbol from the wire-tap channel of type II with two users.The t-wise intersection is a useful property of a linear code due to its many applications. Recently, the t-wise intersection of a constant-weight code and the t-wise intersection of a relative two-weight code have been determined respectively. By using this result and generalizing the finite projective geometry method, we will present the t-wise intersection of a relative three-weight code and its applications in this paper.