本文提出了扩展缩短码的新概念 ,研究了线性和非线性扩展缩短码的构造方法 ,对线性和非线性扩展缩短码的性能进行了理论分析 ,并通过 C+ +和 MATLAB相结合的仿真方法 ,分析了扩展缩短码的最小距离、码重分布、不可检错误概率等方面的性能 ,比较了扩展缩短码和原缩短码以及冗余分配方式不同的两种非线性扩展缩短码性能的优劣。结果表明 :扩展缩短码的理论是原 CRC码理论的完善和补充。本研究为 GSM系统提出了一种新的选择方法。在某些要求码率较高但冗余度不变的通信设备中 ,扩展缩短码是较好的选择 This paper presents a new concept of extended shortening codes, studies the construction methods of linear and nonlinear extended shortening codes, and theoretically analyzes the performance of linear and nonlinear extended shortening codes. By the simulation method combining C + + with MATLAB, This paper analyzes the performance of minimum shortening codes, code redistribution and undetected error probability, and compares the performance of two kinds of non-linear spreading shortening codes, which are different shortening codes, shortened codes and redundant allocation ways. The result shows that the theory of expanding shortening code is the improvement and supplement of the original CRC code theory. This study proposes a new selection method for GSM system. In some communication devices that require a higher code rate but the same redundancy, it is a better choice to extend the shortening code