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Making Every Edit Count: Efficient Binary Edit Correction at the Gilbert-Varshamov Bound — arXiv:2611.04023

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.04023
License (as archived): CC0-1.0
Archived: 2026-11-04T19:01:49.163Z
SHA-256 of the archived text: 603a869a464c0db4279a256afcfb05701f4365b5eafec11eea08cb7061623885
Stable URL of this page: https://metraipolis.com/documento/dc_6eeececf6887

How to cite

Making Every Edit Count: Efficient Binary Edit Correction at the Gilbert-Varshamov Bound — arXiv:2611.04023 — arXiv (en), https://arxiv.org/abs/2611.04023 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_6eeececf6887 (Metraipolis archive dc_6eeececf6887, sha256 603a869a464c0db4279a256afcfb05701f4365b5eafec11eea08cb7061623885)

BibTeX

@misc{dc6eeececf6887,
  title = {Making Every Edit Count: Efficient Binary Edit Correction at the Gilbert-Varshamov Bound — arXiv:2611.04023},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.04023},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_6eeececf6887; sha256 603a869a464c0db4279a256afcfb05701f4365b5eafec11eea08cb7061623885},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.04023. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We construct binary codes that attain the classical Gilbert-Varshamov redundancy guarantee for a fixed number of edit errors, with deterministic polynomial-time construction, encoding, and decoding. For every fixed integer $t\ge 1$ and all sufficiently large block lengths $n$, our codes correct any combination of at most $t$ insertions, deletions, and substitutions in total, with redundancy at most $2t\log_2 n+O_t(1)$. All algorithms run in polynomial time in $n$ for fixed $t$, and decoding recovers the original information message. This realizes the classical counting guarantee algorithmically without enumerating the exponentially large space of binary words.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.IT, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2611.04023 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-04T18:38:39.752Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).