用码构造指数吻数格的困难

IF 2.9 3区计算机科学 Q3 COMPUTER SCIENCE, INFORMATION SYSTEMS

IEEE Transactions on Information Theory Pub Date : 2025-07-28 DOI:10.1109/TIT.2025.3593195

Huck Bennett;Alexander Golovnev;Noah Stephens-Davidowitz

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引用次数: 0

摘要

在这篇文章中，我们给出了一些例子，表明从纠错码构造格的几种自然方法通常不会产生最小权值非零码字和最短非零格向量之间的对应关系。从这些例子中，我们得出结论，主要结果在莫斯科J.库姆的两部作品。Th数量。2019年和离散计算。几何学。， 2021)从纠错码构造具有指数亲吻数的格是无效的。最近的预印本（arXiv, 2024），在这个作品的初始版本被公开后，vl发布的也是无效的。因此，显示具有指数亲吻数的晶格族仍然是一个开放的问题（截至2025年7月）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Difficulties Constructing Lattices With Exponential Kissing Number From Codes

In this note, we present examples showing that several natural ways of constructing lattices from error-correcting codes do not in general yield a correspondence between minimum-weight non-zero codewords and shortest non-zero lattice vectors. From these examples, we conclude that the main results in two works of Vlăduţ (Moscow J. Comb. Number Th., 2019 and Discrete Comput. Geom., 2021) on constructing lattices with exponential kissing number from error-correcting codes are invalid. A more recent preprint (arXiv, 2024) that Vlăduţ posted after an initial version of this work was made public is also invalid. Exhibiting a family of lattices with exponential kissing number therefore remains an open problem (as of July 2025).

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来源期刊

IEEE Transactions on Information Theory 工程技术-工程：电子与电气

CiteScore

5.70

自引率

20.00%

发文量

514

审稿时长

12 months

期刊介绍： The IEEE Transactions on Information Theory is a journal that publishes theoretical and experimental papers concerned with the transmission, processing, and utilization of information. The boundaries of acceptable subject matter are intentionally not sharply delimited. Rather, it is hoped that as the focus of research activity changes, a flexible policy will permit this Transactions to follow suit. Current appropriate topics are best reflected by recent Tables of Contents; they are summarized in the titles of editorial areas that appear on the inside front cover.