摘要
运用Galois环和Hensel提升的相关知识给出了多项式xn-λ(其中λ∈Zq,q=pk,p为素数)在Zq[x]中的不可约分解方法,证明了Zq上的常循环码等价于Zq的某一Galois扩环上的循环码,并在此基础上给出了Zq上的常循环码及1生成准扭码的相关性质.
The irreducible decomposition method of x^n=λ （λ∈Zq, q=p^k, p is a prime number） in Zq[x] by the relevant knowledge of Galois rings and Hensel lift was presented. It was proved that the constacyclic codes over Zq is equivalent to a cyclic code of its Galois extension ring. And on this basis, the relevant properties of constacyclic codes and 1-generator quasi-twisted codes were given.
基金
国家自然科学基金资助项目(60973125)
教育部高校博士点基金(200080359003)资助
