伽罗华域上代数运算的最简实现

Simplest Accomplishment of Arithmetic on Galois Fields

从伽罗华域上运算原理出发，提出了域上运算二表法的改进算法和直接查表法。通过对系统数据处理的基本形式以及域上加法恒元和乘法恒元的表示方法的改进，大大减少了查表转换次数，简化了域上乘（除）法运算。通过对算法流程以及ＢＣＨ译码过程计算量的定量比较，说明了改进算法的先进性，并给出了直接查表法及其性能优劣的定量分析数据。

This paper puts forward a modified two-table method and a directly table-searching method to accomplish the algebraic arithmetic on the Galois Field based on the arithmetical principle. The new two-table method consumedly decreases the total number of table-searching and predigests the algorithm for error controlling system. The merit of the improved two-able method is expounded through the quantitative analysis of the arithmetic and calculation quantity. At last,this paper quantificationally compares the directly table-searching method and the two-table method.