利用F[x]-格基约化算法给出了域F上长度为N的m条序列的最短线性移位寄存器(即极小多项式)的综合算法.此算法的计算复杂度为O(N2)次F中乘运算,同时给出了一个极小多项式惟一的充要判别条件,且在极小多项式不惟一时,给出所有的极小多项式的一般形式和当F为有限域时极小多项式的个数. The synthesis algorithm of the shortest linear shift register (ie, minimal polynomial) of m sequences with length N on the field F is given by F [x] - lattice reduction algorithm.The computational complexity of this algorithm is O (N2 ) Times F multiplication operation, at the same time, it gives the only necessary and sufficient condition for a minimal polynomial. When the minimal polynomial is not unique, it gives the general form of all the minimax polynomials and the minimum when F is a finite field The number of polynomials.