Groups and decompositions of codes
- 作者：Yun Liu ; slliuyun@163.com ; slliuyun@sina.com
- 关键词：Decomposition of codes ; Group of codes ; Maximal code ; Rectangular group code ; Variable-length code
- 刊名：Theoretical Computer Science
- 出版年：2012
- 期刊代码：114_03043975
- 类别：cp
- 出版时间：20 July, 2012
- 卷：443
- 期：Complete
- 页码：70-81
- 文件大小：278 K
摘要
In this paper, some relations between the decompositions of codes and the groups of codes are investigated. We first show the existence of an indecomposable, recognizable, and maximal code such that the group is imprimitive, which implies that the answer to a problem put forward by Berstel, Perrin, and Reutenauer in their book 鈥淐odes and Automata鈥?is negative. Then, we discuss a special kind of code, that is, rectangular group codes, and show that a completely simple code is a rectangular group code if and only if it can be decomposed as a composition of a complete and synchronized code and a group code.