Open AccessAn infinite family of Hadamard matrices constructed from Paley type matrices
Author(s) -
Adda Farouk,
Qingwen Wang
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2003815f
Subject(s) - mathematics , hadamard transform , hadamard three lines theorem , hadamard matrix , hadamard's maximal determinant problem , hadamard's inequality , combinatorics , complex hadamard matrix , modulo , conjecture , order (exchange) , matrix (chemical analysis) , prime power , prime (order theory) , hadamard three circle theorem , type (biology) , hadamard product , discrete mathematics , mathematical analysis , ecology , materials science , finance , economics , composite material , biology
An n x n matrix whose entries are from the set {1,-1} is called a Hadamard matrix if HH? = nIn. The Hadamard conjecture states that if n is a multiple of four then there always exists Hadamard matrices of this order. But their construction remain unknown for many orders. In this paper we construct Hadamard matrices of order 2q(q + 1) from known Hadamard matrices of order 2(q + 1), where q is a power of a prime number congruent to 1 modulo 4. We show then two ways to construct them. This work is a continuation of U. Scarpis? in [7] and Dragomir-Z. Dokovic?s in [10].