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Constructions for Circulant and Group‐Developed Generalized Weighing Matrices
Author(s) -
Craigen Robert,
de Launey Warwick
Publication year - 2016
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.21525
Subject(s) - circulant matrix , mathematics , class (philosophy) , combinatorics , order (exchange) , group (periodic table) , type (biology) , algebra over a field , pure mathematics , discrete mathematics , computer science , ecology , chemistry , organic chemistry , finance , artificial intelligence , economics , biology
Abstract An elementary construction yields a new class of circulant (so‐called “Butson‐type”) generalized weighing matrices, which have order N n and weight n 2 , all of whose entries are n th roots of unity, for all positive integers n , N , where n ≤ N . The idea is extended to a wider class of constructions giving various group‐developed generalized weighing matrices.