论 20 阶哈达玛矩阵的增长因子

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED Applied Numerical Mathematics Pub Date : 2025-02-01 DOI:10.1016/j.apnum.2024.01.019

Emmanouil Lardas, Marilena Mitrouli

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引用次数: 0

摘要

这项工作的目的是提供一个完整的列表，列出阶数为 20 的哈达玛矩阵的前六个枢轴可能取的所有值。这是通过确定此类矩阵的某些最小值的可能值，并结合枢轴可以用这些最小值计算这一事实来实现的。我们扩展了已知结果，给出了前五个枢轴可能值的完整列表的不同证明，并确定了第六个枢轴可能值的完整列表。通过使用计算方法寻找新的枢轴模式，我们还发现了至少 1246 种不同的哈达玛矩阵 20 阶枢轴模式。

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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On the growth factor of Hadamard matrices of order 20

The aim of this work is to provide a complete list of all the possible values that the first six pivots of an Hadamard matrix of order 20 can take. This is accomplished by determining the possible values of certain minors of such matrices, in combination with the fact that the pivots can be computed in terms of these minors. We extend known results, by giving a different proof for the complete list of possible values for each of the first five pivots, as well as determining the complete list of possible values for the sixth pivot. By using a computational approach to search for new pivot patterns, we have also found at least 1246 different pivot patterns of Hadamard matrices of order 20.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.