Isometric embeddings of finite fields
Isometric embeddings of finite fields
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有限域的等距嵌入
DOI：
10.1016/j.ffa.2013.09.003
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发表时间：
2014
影响因子：
1
通讯作者：
Yasushi Mizusawa and Shinya Nishikawa
中科院分区：
文献类型：
--
作者：
C.H. Lam;H. Shimakura;山田 裕理;毛利 猛;木村巌;D. Sagaki & H. Shimakura;Yasushi Mizusawa and Shinya Nishikawa
通过将有限域看作素域上的向量空间，其基由元素的幂构成，定义了有限域上关于幂基的汉明距离。我们考虑了这类有限域之间的等距同态的存在性，并利用算术条件刻画了偶特征的等距嵌入。此外，在有限域的某个无限维代数扩张上定义了一个标准Hamming度量。
By regarding a finite field as a vector space over the prime field with a basis consisting of powers of an element, a Hamming distance is defined on the finite field with respect to the power basis. We consider the existence of isometric homomorphisms between such finite fields, and characterize the isometric embeddings for even characteristic by arithmetical conditions. Moreover, a canonical Hamming metric is defined in a certain infinite dimensional algebraic extension of a finite field.