为了设计合适的线性网络编码以提高多源多中继系统的分集增益性能，从理论上研究了系统分集增益与网络编码最小码距的关系，提出以最小码距作为线性网络编码的设计准则. 利用经典线性分组码的有关理论和分析方法，得出了系统的分集增益等于线性网络编码的最小码距这一重要命题，该命题将原网络编码的设计问题转化为最小码距准则下经典线性分组码的设计问题. 另外，根据编码理论的singleton界得到了系统最大分集增益与中继节点数目之间的定量关系. 仿真实验表明，增大网络编码的最小码距能够提高系统的分集增益，而系统的最大分集增益等于中继数加1.

To design a linear network code and increase diversity gain of multi-source multi-relay system, this paper investigates relationship between diversity gain and minimum hamming distance of network code, and proposes a method that using minimum hamming distance as the design criterion of linear network code. By using related theories and methods of classic linear block code, an important proposition that system diversity gain is equal to minimum hamming distance is derived. Based on this proposition, the original problem of designing network code is converted to designing classic linear block codes under minimum hamming distance criterion. In addition, based on the singleton bound in the classic coding theory, quantitative relationship between maximum diversity and relay number is obtained. Simulation results show that the diversity gain is improved by increasing the minimum hamming distance and the maximum diversity gain is equal to the total number of relays plus 1.