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Pré-Publication, Document De Travail Année : 2022

When Variable-Length Codes Meet the Field of Error Detection

Jean Néraud

Résumé

Given a finite alphabet $A$ and a binary relation $\tau\subseteq A^*\times A^*$, a set $X$ is $\tau$-{\it independent} if $ \tau(X)\cap X=\emptyset$. Given a quasi-metric $d$ over $A^*$ (in the meaning of \cite{W31}) and $k\ge 1$, we associate the relation $\tau_{d,k}$ defined by $(x,y)\in\tau_{d,k}$ if, and only if, $d(x,y)\le k$ \cite{CP02}. In the spirit of \cite{JK97,N21}, the error detection-correction capability of variable-length codes can be expressed in term of conditions over $\tau_{d,k}$. With respect to the prefix metric, the factor one, and every quasi-metric associated to (anti-)automorphisms of the free monoid, we examine whether those conditions are decidable for a given regular code.
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Dates et versions

hal-03764465 , version 1 (30-08-2022)
hal-03764465 , version 2 (05-10-2022)

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Jean Néraud. When Variable-Length Codes Meet the Field of Error Detection. 2022. ⟨hal-03764465v2⟩
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