2023/09/05 by Jean Néraud, Néraud, Jean
Computer Science · Immunology and Microbiology · #Coding theory and cryptography #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Immunodeficiency and Autoimmune Disorders #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2309.01997
openalex publication_date 2023/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Given a finite alphabet A, a quasi-metric d over A^*, and a non-negative integer k, we introduce the relation τd,k⊆ A^*× A^* such that (x,y)∈τd,k holds whenever d(x,y)≤ k. The error detection capability of variable-length codes is expressed in term of conditions over τd,k. With respect to the prefix metric, the factor one, and any quasi-metric associated with some free monoid (anti-)automorphism, we prove that one can decide whether a given regular variable-length code satisfies any of those error detection constraints.