| 摘要: |
| 设q为素数的方幂，n(≥2)为正整数，给出了模qn-1的q-循环的一些性质，并利用这些性质讨论了F2n到F2上一类特殊正规基的存在性，最后证明了n=4时，这类正规基可为Ⅰ型最优正规基；n≠4时，它一定不是最优正规基. |
| 关键词: 有限域 正规基 q-循环 |
| DOI： |
| 分类号: |
| 基金项目: |
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| A Class of Normal Bases on Binary Field and q Cycle |
|
LI Bo
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| Abstract: |
| Let q be the power of a prime p，n(≥2)be an integer.Some properties of q cycle modular qn 1are given.With these properties this paper discusses the existence of a kind of special normal bases from F2n to F2.Finally，it is proved that this kind of special normal bases can be optimal normal bases of type Ⅰ，if n=4；Otherwise，it can't be optimal normal bases. |
| Key words: finite fields,normal bases,q cycle |
