A search for solvable weighing matrices

Paul Becker, Sheridan Houghten, Wolfgang Haas

Research output: Contribution to journalArticle

Abstract

A weighing matrix W(n, k) of order n with weight k is an n × n matrix with entries from {0, 1, - 1} which satisfies WWT = kIn. Such a matrix is group-developed if its rows and columns can be indexed by elements of a finite group G so that ω g,h = ωgf, hf for all g, h, and f in G. Group-developed weighing matrices are a natural generalization of perfect ternary arrays and Hadamard matrices. They are closely related to difference sets. We describe a search for weighing matrices with order 60 and weight 25, developed over solvable groups. There is one known example of a W(60, 25) developed over a nonsolvable group; no solvable examples are known. We use techniques from representation theory, including a new viewpoint on complementary quotient images, to restrict solvable examples. We describe a computer search strategy which has eliminated two of twelve possible cases. We summarize plans to complete the search.

Original languageEnglish (US)
Pages (from-to)65-84
Number of pages20
JournalJournal of Combinatorial Mathematics and Combinatorial Computing
Volume62
StatePublished - Aug 1 2007

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Weighing Matrices
Difference Set
Hadamard Matrix
Solvable Group
Search Strategy
Representation Theory
Ternary
Quotient
Finite Group

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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A search for solvable weighing matrices. / Becker, Paul; Houghten, Sheridan; Haas, Wolfgang.

In: Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 62, 01.08.2007, p. 65-84.

Research output: Contribution to journalArticle

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