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On the $b$-Symbol Weight Distribution of Dual Melas Codes and a Poisson Randomness Postulate — arXiv:2610.38017

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.38017
License (as archived): CC0-1.0
Archived: 2026-11-01T02:39:37.743Z
SHA-256 of the archived text: da5007937c90f1af5c3bd5c4ade7248d4ffd3f5c804432549e5eeba03af98113
Stable URL of this page: https://metraipolis.com/documento/dc_03445ccdce5a

How to cite

On the $b$-Symbol Weight Distribution of Dual Melas Codes and a Poisson Randomness Postulate — arXiv:2610.38017 — arXiv (en), https://arxiv.org/abs/2610.38017 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_03445ccdce5a (Metraipolis archive dc_03445ccdce5a, sha256 da5007937c90f1af5c3bd5c4ade7248d4ffd3f5c804432549e5eeba03af98113)

BibTeX

@misc{dc03445ccdce5a,
  title = {On the $b$-Symbol Weight Distribution of Dual Melas Codes and a Poisson Randomness Postulate — arXiv:2610.38017},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.38017},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_03445ccdce5a; sha256 da5007937c90f1af5c3bd5c4ade7248d4ffd3f5c804432549e5eeba03af98113},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.38017. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove a new lower bound on the $b$-symbol weight of codewords in dual Melas codes, which is strictly better than known results. We employ a new strategy that translates a pattern counting problem in linear-feedback shift register sequences to a problem on orbits of binary polynomials under a certain action. We use the same techniques to provide an improved lower bound on the burst-covering radius of Melas codes and a new upper bound on the critical exponent of dual Melas codes. We then define a new randomness postulate on (families of) binary sequences, based on the definition of infinite Poisson generic sequences. We conjecture that codewords in the dual Melas code satisfy this postulate, and we show partial progress in establishing this conjecture. We also show how a relaxed version of the problem can be completely resolved, and relate the conjecture to the first part of the paper, giving a justification of why the improved bounds on the $b$-symbol weight were somewhat to be expected.

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/2610.38017 — 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 2026-11-01T02:15:43.717Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).