环F_p+uF_p Galois扩张上的迹码

Trace codes over Galois extension of ring F_p+uF_p

给出了环Fp+uFp(p为任意素数)的Galois扩张的相关理论,定义了Galois扩环上的迹码及子环子码的概念,证明了此Galois扩环上对偶码的迹码是该环的子环子码的对偶码.

In this paper,we give some theorists about the Galois extension of ring Fp+uFp,and give the definitions of the trace codes and subring subcodes on this Galois extension ring.Moreover,we prove that the trace codes of dual codes are the dual of subring subcodes.