中文摘要：

有限域F_q上r维向量空间F_q~r中的极大n元t-无关组是一个很重要的组合结构,可以用来构造强部分平衡设计,从而可构造最优认证码;也可用来构造正交阵列.本文揭示有限域F_2上r维向量空间F_2~r中极大3无关组的函数特征,即每一个极大3无关组恰好是某个线性函数的支撑.

英文摘要：

The maximal （n, t） linearly independent array of vector space Fqr over finite field Fq is an important combinatorial structure, which can be used to construct strong partial balanced design, optimal authentication scheme, orthogonal array, and so on. In this paper, we provide a functional characteristic of the maximal 3 linearly independent array, every of which is exactly the support of some linear function.