数学季刊 ›› 2016, Vol. 31 ›› Issue (1): 60-68.doi: 10.13371/j.cnki.chin.q.j.m.2016.01.008
摘要: Under the assumption that the wiretapper can get at most r(r < n) independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q-1. They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the(n- r) ×(n- r)and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction.
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