THERMAL SCIENCE

International Scientific Journal

Shu-Hui Shen

,

Mao-Bo Zheng

AN INFINITE CLASS OF HADAMARD MATRICES OF ORDER 4(Q+1) OF GOETHALS-SEIDEL TYPE

ABSTRACT
In this paper, we construct a new infinite class of Hadamard matrices of Goethals-Seidel (GS) type. Using Parseval relations with coefficients of four polynomials and the properties in the Galois fields, we obtain the first rows of these four circulant matrices of order q+1, with a prime power q≡ 1(mod4), and further the desired matrices.
KEYWORDS
Hadamard matrices, GS type, Parseval relation
PAPER SUBMITTED: 2025-08-08
PAPER REVISED: 2025-09-27
PAPER ACCEPTED: 2025-11-12
PUBLISHED ONLINE: 2026-07-25
DOI REFERENCE: https://doi.org/10.2298/TSCI250808139S
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An infinite class of Hadamard matrices of order 4(Q+1) of Goethals-Seidel type

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International licence