# When Variable-Length Codes Meet the Field of Error Detection

arXiv: https://arxiv.org/abs/2208.14681 · HTML: https://mlsanity.com/paper/2208.14681/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 31 references that are in the map.
- First posted on arXiv 31 Aug 2022.

## Builds on (most cited first, 2 of 2)

- [Embedding a θ-invariant code into a complete one](https://mlsanity.com/paper/1801.05164/) (2018)
- [Variable-Length Codes Independent or Closed with respect to Edit Relations](https://mlsanity.com/paper/2104.14185/) (2021)

## Abstract (arXiv)

Given a finite alphabet A and a binary relation τsubseteq A^*× A^*, a set X is τ-it independent if  τ(X)cap X=emptyset. Given a quasi-metric d over A^* (in the meaning of citeW31) and k≥ 1, we associate the relation τd,k defined by (x,y)∈τd,k if, and only if, d(x,y)≤ k citeCP02.In the spirit of citeJK97,N21, the error detection-correction capability of variable-length codes can be expressed in term of conditions over τd,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.