前缀码及其两个子类的代数性质

发布时间：2018-03-27 23:14

本文选题：前缀码　切入点：偏序关系　出处：《西北大学学报(自然科学版)》2014年06期

【摘要】：从(2,2)-型代数的角度研究前缀码的两个子类的代数性质并探讨它们的生成机制。利用自由半群上的偏序关系引入两个前缀码的子类;在这些形式语言类上分别添加二元运算,得到(2,2)-型代数,利用半环的代数理论讨论其代数性质。结果表明,这两个(2,2)-型代数是半环,由此阐明了这两类前缀码的生成机制。从而说明自由半群上的偏序关系是构造码的有力工具。此外,借助经典的代数运算可以建立不同码之间的联系。
[Abstract]:In this paper, the algebraic properties of two subclasses of prefix codes and their generating mechanisms are studied from the point of view of the algebras of the two prefixes. The subclasses of the two prefixes are introduced by using the partial order relation on the free Semigroups, and the binary operations are added to the classes of these formal languages, respectively. The algebraic properties of these algebras are discussed by using the algebraic theory of semirings. The results show that these two algebras are semirings. The generating mechanism of these two kinds of prefix codes is explained. It is shown that the partial ordering on free Semigroups is a powerful tool for constructing codes. In addition, the relations between different codes can be established by means of classical algebraic operations.
【作者单位】：西安理工大学理学院;
【基金】：国家自然科学基金资助项目(61402364) 陕西省自然科学基金资助项目(2014JQ1014)
【分类号】：TN911.2

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