摘要
该文利用环同态理论,给出了环kq+uFq+…+u(k-1)Fq上任意长度N的所有(uλ-1)-常循环码的生成元,l是R的可逆元。证明了R[x]/1是主理想环。给出了环R上任意长度N的(uλ-1)-常循环码的计数。确定了环R上任意长度N的(uλ-1)-常循环码的最高阶挠码的生成多项式,由此给出了环R上长度ps的所有(uλ-1)-常循环码的汉明距离。
Let R denote the ring kq+uFq+…+u(k-1)Fq,and λ be an invertible element of R.By means of the theory of ring homomorphism,the generators of all these(uλ-1)-constacyclic codes of an arbitrary length N over the ring R are obtained.It is proved that R[x]/1 is principal.The number of these(uλ-1)-constacyclic codes is determined.The generator polynomials of the highest-order torsion codes of all these(uλ-1)-constacyclic codes are given.As a result,the Hamming distances of all these(uλ-1) constacyclic codes are obtained.
引文
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