基于可变拟阵搜索算法构造码率为1/p的二进制系统准循环码

Construct the Systematic Binary Quasi-cyclic Codes with Rate 1/p Based on Variable Matroid Search Algorithm

该文针对拟阵搜索算法复杂度高以及局部拟阵搜索算法无法搜索到全部最优码的问题,通过研究拟阵搜索算法,提出可变拟阵搜索算法,并用于搜索准循环码。该算法通过减少重复搜索从而降低运算复杂度;基于该算法构造码率为1/p的二进制系统准循环码,随着整数p的变化,生成矩阵减少或者增加一个循环矩阵,产生码率均为1/p的最优码。通过实验得到两个最小距离比现有最优码更大的准循环码,表明算法的可行性和优越性。

Because the matroid search algorithm is very complicated and the local matroid search algorithm can not search all optimal codes, this paper proposes a variable matroid search algorithm to search the quasi-cyclic codes by researching matroid search algorithm. The algorithm reduces the computational complexity by reducing the repeated search. Based on this algorithm, the systematic binary quasi-cyclic codes of which the rate is 1/p are constructed. With the change of integer p, the optimal codes of rate 1/p can be obtained by the generator matrix reducing or adding a loop matrix. Through experiments, two new codes of which the minimum distance is larger than the existing optimal codes are worked out, which indicate the feasibility and superiority of the algorithm.