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应用科学学报 ›› 1987, Vol. 5 ›› Issue (4): 308-316.

• 论文 • 上一篇    下一篇

关于纠两个错误的二元Goppa码的准完备性及其完全译码

冯贵良   

  1. 上海计算技术研究所
  • 收稿日期:1984-02-18 修回日期:1985-01-02 出版日期:1987-12-31 发布日期:1987-12-31

ON QUASI-PERFECT PROPERTY OF DOUBLE-ERROR-CORRECTING GOPPA CODES AND THEIR COMPLETE DECODING

FENG GUILIANG   

  1. Shanghai Institute of Computer Technology
  • Received:1984-02-18 Revised:1985-01-02 Online:1987-12-31 Published:1987-12-31

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摘要： 本文证明了位置集L=GF(2m)、生成多项式G(z)=z2+az+b的二元Goppa码,除m为偶数并且S1=0,S3=a-1外,是准完备的.当m为偶数,那末不存在重量不大于3的矢量具有伴随式S1=0,S3=a-1;但至少存在一个重量为4的矢量具有伴随式S1=0,S3=a-1,此外,还给出L=GF(2m)、G(z)=z2+az+b的二元Goppa码的一个完全译码.

Abstract: In this paper, we prove that the binary Goppa codes with L=GF(2m) and G(z)=z2+az+b are quasi-perfect unless m is even and S1=0,S3=a-1. When m is even, there is not any vector of weight <3 having syndrome S1=0 and S3=a-1 but there is at least a vector of weight 4 having syndrome S1=0 and S3=a-1. At the same time we give also a complete decoding of the binary Goppa codes with L=GF(2m) and G(z)=z2+az+b.