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| 摘要: |
| 本文研究了环F2+vF2上的循环码.利用标准形生成元集刻画了环F2+vF2上的循环码的代数结构,证明了环F2+vF2上的每一个非零的循环码均有唯一的标准形生成元集,进而得到了每一个循环码均是由一个多项式生成的. |
| 关键词: 环F2+vF2 循环码 标准形生成元集 |
| DOI： |
| 分类号:O157.4 |
| 基金项目:国家自然科学基金资助(11171370;11301254);河南省基础与前沿技术研究计划项目(132300410313);河南省教育厅科学技术研究重点项目(13A110800). |
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| CYCLIC CODES OVER F2+vF2 |
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ZHANG Guang-hui,LI Liang-chen
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| Abstract: |
| In this paper, cyclic codes over F2+vF2 are studied. By virtue of the generating set in standard form for the cyclic codes over F2+vF2, we characterize the structure of cyclic codes over the ring. Then we prove that any nonzero cyclic code over the ring has a unique generating set in standard form and they are principally generated. |
| Key words: F2+vF2 cyclic codes generating set in standard form |
