Abstract
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.
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