环Fpm+uFpm上长为pk的循环码计数
doi: 10.3724/SP.J.1146.2009.01325
Mass Formulas for Cyclic Codes of Lengthpk over the Ring Fpm+uFpm
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摘要: 环R=Fpm+uFpm上长为pk的循环码可看作R[x]/xpk-1上的理想。该文通过对R[x]/xpk-1上理想的研究，得到了环Fpm+uFpm上长为pk的循环码的唯一表示方法和计数，并给出了该环上长为pk的循环自对偶码的结构和计数。Abstract: Cyclic codes over the ringR=Fpm+uFpm can be seen as the ideals of R[x]/xpk-1. Based on the studing of ideals of R[x]/xpk-1, a unique method of representing cyclic codes of lengthpk and their mass formulas over the ringFpm+uFpm are provided. For the cyclic self-dual codes of lengthpk over the ring Fpm+uFpm, their structures and mass formulas are given.
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Key words:
- Cyclic codes /
- Self-dual codes /
- Annihilator
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