A generalization of circulant Hadamard and conference matrices
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA2001XZ3" target="_blank" >RIV/61988987:17310/19:A2001XZ3 - isvavai.cz</a>
Alternative codes found
RIV/61389005:_____/19:00504072
Result on the web
<a href="https://www.sciencedirect.com/science/article/abs/pii/S0024379519300424" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S0024379519300424</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2019.01.018" target="_blank" >10.1016/j.laa.2019.01.018</a>
Alternative languages
Result language
angličtina
Original language name
A generalization of circulant Hadamard and conference matrices
Original language description
We study the existence and construction of circulant matrices C of order n≥2 with diagonal entries d≥0, off-diagonal entries ±1 and mutually orthogonal rows. These matrices generalize circulant conference (d=0) and circulant Hadamard (d=1) matrices. We demonstrate that matrices C exist for every order n and for d chosen such that n=2d+2, and we find all solutions C with this property. Furthermore, we prove that if C is symmetric, or n-1 is prime, or d is not an odd integer, then necessarily n=2d+2. Finally, we conjecture that the relation n=2d+2 holds for every matrix C, which generalizes the circulant Hadamard conjecture. We support the proposed conjecture by computing all the existing solutions up to n=50.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
LINEAR ALGEBRA APPL
ISSN
0024-3795
e-ISSN
—
Volume of the periodical
569
Issue of the periodical within the volume
15 May 2019
Country of publishing house
US - UNITED STATES
Number of pages
25
Pages from-to
241-265
UT code for WoS article
000462111500013
EID of the result in the Scopus database
2-s2.0-85060895400