Legendre pairs of lengths ℓ ≡ 0 (mod 5)

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2023-01-01 DOI:10.1515/spma-2023-0105

Ilias S. Kotsireas, Christoph Koutschan, Dursun A. Bulutoglu, David M. Arquette, Jonathan S. Turner, Kenneth J. Ryan

引用次数: 1

Abstract

Abstract By assuming a type of balance for length ℓ = 87 \ell =87 and nontrivial subgroups of multiplier groups of Legendre pairs (LPs) for length ℓ = 85 \ell =85 , we find LPs of these lengths. We then study the power spectral density (PSD) values of m m compressions of LPs of length 5 m 5m . We also formulate a conjecture for LPs of lengths ℓ ≡ 0 \ell \equiv 0 (mod 5) and demonstrate how it can be used to decrease the search space and storage requirements for finding such LPs. The newly found LPs decrease the number of integers in the range ≤ 200 \le 200 for which the existence question of LPs remains unsolved from 12 to 10.

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长度为0 (mod 5)的Legendre对

摘要通过假设长度为z =87 \ell =87的一类平衡和长度为z =85 \ell =85的Legendre对乘子群的非平凡子群，我们得到了这些长度的lp。然后，我们研究了长度为5m ～ 5m的lp的m ～ m压缩的功率谱密度(PSD)值。我们也为长度为r≡0 \ell\equiv 0 (mod 5)的lp制定了一个猜想，并演示了如何使用它来减少查找此类lp的搜索空间和存储需求。新发现的LPs使≤200 \le 200范围内存在性问题未解决的整数从12个减少到10个。

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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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.