Maximal Bifix Codes of Degree 3

作者：Bai, Liyan; Jin, Lianyan; Liu, Yun^*

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41(3): 1393-1407.

DOI：10.1007/s40840-016-0399-y

• Maximal bifix code
• Degree of codes
• Prefix code
• Enumeration
• Directed acyclic graph

The construction of thin maximal bifix codes of degree 1 or 2 is clear and simple. In this paper, a class of thin maximal bifix codes of degree 3 which contains all finite maximal bifix codes of degree 3 is investigated. The construction of such codes is determined. It is well known that for any positive integers d and k, there are finitely many finite maximal bifix codes of degree d over a k-letter alphabet. But the enumeration problem is unsolved in general. In this paper, we show that for any positive integer k, there is a bijection from the set of all finite maximal bifix codes of degree 3 over a k-letter alphabet onto the set of all directed acyclic graphs with k vertices, and then, the enumeration problem of finite maximal bifix codes of degree 3 is solved.

• 出版日期2018-7
• 单位玉溪师范学院