一类代数几何码的伴随式阵列

主要讨论了一点代数几何码的伴随式阵列及其上的线性递推关系。通过缩简多项式概念的建立和理想这个数学概念的运用，将译码时真正需要的线性递推关系和这种伴随式阵列固有的线性递推关系区别开来，达到了从一点代数几何码的伴随式阵列的线性递推关系中将其固有的线性递推关系剔除掉的目的。在定理５的证明中还蕴涵了寻找一个多项式的缩减多项式的算法，这些结果对进一步研究Ｆｅｎｇ等提出的译码算法和Ｓｋａｔａ等提出的译码算法有

On the Syndrome Arrays of a Class of Algebraic-Geometric Codes

The syndrome arrays ar e discussed in detail which are employed in decoding of a class of alge braic geometric codes and the linear recurring relations on that.By establishin g the concept of reduced simplified polynomial and applying the algebraic concept of idea in polynomial ring, we can distinguish the linear recurring relations g enuinely needed in decoding from the inherent ones on the syndrome arrays.And we clarify ambiguities occurred in [1],achieving the goal of deleting the inhere nt ones from t he linear recurring relations on the syndrome arrays. From the proof of Theorem 5 one can construct an algorithm of finding a reduced simplified polynomial of a polynomial. Thes e results are helpful to further investigate the decoding algorithms proposed by Feng et al.and by Sakata et al.