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文章约定R=F_q+uF_q+u~2F_q+…+u~(k-1)F_q,其中u~k=0,q为某一素数幂,研究环R上的线性码关于齐次度量的完备性,得到了环R上的线性码的球形填充界,并且利用这些界去检验线性码的完备性,讨论了环R上2种特殊情况下关于齐次度量的完备线性码的存在性。
The paper holds that R = F_q + uF_q + u ~ 2F_q + ... + u ~ (k-1) F_q, where u ~ k = 0, q is a prime power and the completeness of the linear codes on the R ring , We obtain the spherical filling bounds of linear codes on ring R, and use these bounds to test the completeness of linear codes. We discuss the existence of perfect linear codes for homogeneous measurements in two special cases on ring R.