On codes with a finite deciphering delay: constructing uncompletable words

Carla Selmi (1) , Jean Néraud (1)

1 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

Let X a non-complete code with a finite dechiphering delay. We prove that an uncompletable word w of length O(n²d²) exists, where d stands for the delay and m stands for the length of the longest word in X. The proof leads to an explicit construction of w. This result partially resolves a conjecture proposed by Antonio Restivo in 1979.

Mots clés: Code; Prefix code; Uniform code; Dechiphering delay; Complet subset; Uncompletable word

Domaines: Informatique et langage [cs.CL]; Théorie de l'information [cs.IT]; Théorie de l'information et codage [math.IT]

Carla Selmi, Jean Néraud. On codes with a finite deciphering delay: constructing uncompletable words. Theoretical Computer Science, 2001, 255, pp.151-162. ⟨hal-00460320⟩