2017/05/16 by Jean Néraud, Néraud, Jean, Carla Selmi +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #DNA and Biological Computing #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.DM #cs.IT #math.CO #math.IT
paper · pdf · doi:10.48550/arxiv.1705.05564
To appear in Acts of WORDS 2017
openalex publication_date 2017/05/16 · arxiv created 2017/07/27 · arxiv updated 2017/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a finite or countable alphabet and let θ be literal (anti)morphism onto A^* (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under θ (θ-invariant for short).We establish an extension of the famous defect theorem. Moreover, we prove that for the so-called thin θ-invariant codes, maximality and completeness are two equivalent notions. We prove that a similar property holds in the framework of some special families of θ-invariant codes such as prefix (bifix) codes, codes with a finite deciphering delay, uniformly synchronized codes and circular codes. For a special class of involutive antimorphisms, we prove that any regular θ-invariant code may be embedded into a complete one.