环k_q+uF_q+…+u^(k-1)F_q上任意长度的(uλ-1)-常循环码

(uλ-1)-constacyclic Codes of Arbitrary Lengths over the Ring k_q+uF_q+…+u^(k-1)F_q

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<xN+-uλ>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 R = Fq ＋ uFq ＋... ＋ uk-1Fq, and ）λ be an invertible element of R. By means of the theory of ring homomorphism, the generators of all these （uA - 1） - constacyclic codes of an arbitrary length N over the ring R are obtained. It is proved that R[x] / 〈 xN ＋ 1 - uλ〉 is principal. The number of these （u）λ - 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.