Abstract: 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.

Key words: network coding, cooperative communication,  minimum hamming distance, diversity gain