环Fq+uFq++uk1Fq上任意长度的(u1)-常循环码
doi: 10.3724/SP.J.1146.2012.01257
(u1)-constacyclic Codes of Arbitrary Lengths over the Ring Fq+uFq++uk1Fq
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摘要: 该文利用环同态理论，给出了环R=Fq+uFq++uk1Fq上任意长度N的所有(u1)-常循环码的生成元，是R的可逆元。证明了R[x]xN+1u是主理想环。给出了环R上任意长度N的(u1)-常循环码的计数。确定了环R上任意长度N的(u1)-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(u1)-常循环码的汉明距离。Abstract: Let R denote the ring R=Fq+uFq++uk1Fq , and be an invertible element of R. By means of the theory of ring homomorphism, the generators of all these (u1)-constacyclic codes of an arbitrary length N over the ring R are obtained. It is proved thatR[x]xN+1u is principal. The number of these (u1)-constacyclic codes is determined. The generator polynomials of the highest-order torsion codes of all these (u1)-constacyclic codes are given. As a result, the Hamming distances of all these (u1)-constacyclic codes are obtained.
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Key words:
- Constacyclic codes /
- Highest-order Torsion codes /
- Negacyclic codes /
- Hamming distances
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