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Hadamard Matrices Modulo 5
Author(s) -
Lee Moon Ho,
Szöllősi Ferenc
Publication year - 2014
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21369
Subject(s) - modulo , hadamard transform , mathematics , hadamard matrix , conjecture , complex hadamard matrix , modular design , combinatorics , order (exchange) , hadamard three lines theorem , arithmetic , discrete mathematics , computer science , mathematical analysis , finance , economics , operating system
In this paper, we introduce modular symmetric designs and use them to study the existence of Hadamard matrices modulo 5. We prove that there exist 5‐modular Hadamard matrices of order n if and only if n ¬ ≡ 3 , 7 ( mod10 ) or n ≠ 6 , 11 . In particular, this solves the 5‐modular version of the Hadamard conjecture.