域上的自同构线性变换

A isomorphic linear transformation on domain

域是一个重要的代数系统 ,特别是有限域在编码理论 ,拉丁方的构造及区组设计等方面均有着广泛的应用 ,域具有所谓加法和乘法的两种运算 ,并且域中有两个特异元素—零元和幺元 ,本文通过一种自同构变换 ,诱导出两种新的运算 ,从而形成一个与该域同构的域 .对域中任意的两个不同元素 。

The domain is an important algebra system, especially the limited domain has been widely used in coding theory,formation of Litin square and block design.Besides the two operations in the domain,which are called addition and multiplication,there are two special elements in domain,zero and unity.In this paper,an isomorphic transformation is introduced to derivate two new operations,and a new domain with the same configuration is formed.For any twodifferent elements in the domain,they can be assigned as zero and unity in the new domain respectively.