A Note with Computer Exploration on the Triangle Conjecture
The triangle conjecture states that codes formed by words of the form \(a^i b a^j\) are either commutatively equivalent to a prefix code or not included in a finite maximal code. Thanks to computer exploration, we exhibit new examples of such non-commutatively prefix codes. In particular, we improve a lower bound in a bounding due to Shor and Hansel. We discuss in the rest of the article the possibility of those codes to be included in a finite maximal code.
KeywordsCodes Triangle conjecture Commutative equivalence conjecture
The author wants to thank Dominique Perrin for introducing him to the commutatively prefix conjecture, also his Ph.D. supervisors Samuele Giraudo and Jean-Christophe Novelli.
- 7.Sardinas, A.A., Patterson, G.W.: A necessary and sufficient condition for unique decomposition of coded messages. In: Proceedings of the Institute of Radio Engineers, vol. 41, no. 3, pp. 425–425 (1953)Google Scholar