Abstract: Applying the rules of polynomial in finite field，operation modules which can carry out addition，multiplication，inverse calculation in GF（2⁸） were designed with MATLAB software.And an RS codec software based on these operation modules was implemented using modified Euclid’s algorithm（MEA） and Fast Fourier Transformation in finite field.This software can accommodate to both different primitive polynomials over GF（2ⁿ） with n≤8 and different error correction capabilities.The simulation result shows that the RS（255，223） decoder software has such advantages as high efficiency to meet the demand of real-time communication transmission.So it will be served as an efficient auxiliary technique for algorithm development and verification together with hardware design and debugging.

Key words: Reed-Solomon, RS decoding, modified Euclid's algorithm

摘要： 遵循有限域上多项式的运算规则，使用MATLAB软件设计了GF（2⁸）上的加法、乘法、求逆运算模块，并以这些模块为基础，采用修正的欧几里德算法（MEA）与有限域上快速傅立叶变换算法相结合的思想，实现了RS（255，223）的软件译码。此软件参数可调，可以适应GF（2ⁿ）域（n≤8）上不同本原多项式、不同纠错能力的RS码，具有很强的通用性。仿真结果表明，所设计的RS（255，223）译码软件运行效率高，满足实时通信传输需要；并为算法开发、验证和硬件设计调试提供了一种强有力的辅助手段。

关键词: 里德-索罗蒙码, RS译码, 修正的欧几里德算法